The construction of control Lyapunov functions for a class of nonlinear systems is considered. We develop a method by which a control Lyapunov function for the feedback linearizable part can be constructed systematica...The construction of control Lyapunov functions for a class of nonlinear systems is considered. We develop a method by which a control Lyapunov function for the feedback linearizable part can be constructed systematically via Lyapunov equation. Moreover, by a control Lyapunov function of the feedback linearizable part and a Lyapunov function of the zero dynamics, a control Lyapunov function for the overall nonlinear system is established.展开更多
A method is developed by which control Lyapunov functions of a class of nonlinear systems can be constructed systematically. Based on the control Lyapunov function, a feedback control is obtained to stabilize the clos...A method is developed by which control Lyapunov functions of a class of nonlinear systems can be constructed systematically. Based on the control Lyapunov function, a feedback control is obtained to stabilize the closed-loop system. In addition, this method is applied to stabilize the Benchmark system. A simulation shows the effectiveness of the method.展开更多
The stabilization of discrete nonlinear systems is studied. Based on control Lyapunov functions, a sufficient and necessary condition for a quadratic function to be a control Lyapunov function is given. From this cond...The stabilization of discrete nonlinear systems is studied. Based on control Lyapunov functions, a sufficient and necessary condition for a quadratic function to be a control Lyapunov function is given. From this condition, a continuous state feedback law is constructed explicitly. It can globally asymptotically stabilize the equilibrium of the closed-loop system. A simulation example shows the effectiveness of the proposed method.展开更多
The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain syst...The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality （LMI） conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances.展开更多
The problem of robust L 1 filtering with pole constraint in a disk for linear continuous polytopic uncertain systems is discussed. The attention is focused on design a linear asymptotically stable filter such that th...The problem of robust L 1 filtering with pole constraint in a disk for linear continuous polytopic uncertain systems is discussed. The attention is focused on design a linear asymptotically stable filter such that the filtering error system remains robustly stable, and has a L 1 performance constraint and pole constraint in a disk. The new robust L 1 performance criteria and regional pole placement condition are obtained via parameter-dependent Lyapunov functions method. Upon the proposed multiobjective performance criteria and by means of LMI technique, both full-order and reduced-order robust L 1 filter with suitable dynamic behavior can be obtained from the solution of convex optimization problems. Compared with earlier result in the quadratic framework, this approach turns out to be less conservative. The efficiency of the proposed technique is demonstrated by a numerical example.展开更多
The thermal power boiler-turbine system is a complex system with high nonlinearity,time-delay and strong coupling.It is difi cult to obtain an excellent dynamic response by means of traditional PI/PID control when the...The thermal power boiler-turbine system is a complex system with high nonlinearity,time-delay and strong coupling.It is difi cult to obtain an excellent dynamic response by means of traditional PI/PID control when the power system load changes in a wide range.So far many advanced control strategies have been presented to solve the above problem,but most of these strategies are dependent on an accurate object model.展开更多
This research focuses on detecting faults in flight vehicles with unstable subsystems operating asynchronously.By accounting for asynchronous switching,a switched model is established,and filters for fault detection(F...This research focuses on detecting faults in flight vehicles with unstable subsystems operating asynchronously.By accounting for asynchronous switching,a switched model is established,and filters for fault detection(FD)in unstable subsystems are developed.The FD challenge is then transformed into an H∞filtering issue.Utilizing the multiple discontinuous Lyapunov function(MDLF)approach and the mode-dependent average dwell time(MDADT)method,sufficient conditions are derived to ensure stability during both fast and slow switching.Furthermore,the existence and solutions for FD filters are provided through linear matrix inequalities(LMIs).The simulation outcomes demonstrated the excellent performance of the developed method in studied cases.展开更多
The problem of adaptive stabilization of a class of multi-input nonlinear systems with unknown parameters both in the state vector-field and the input vector-field has been considered. By employing the control Lyapuno...The problem of adaptive stabilization of a class of multi-input nonlinear systems with unknown parameters both in the state vector-field and the input vector-field has been considered. By employing the control Lyapunov function method, a direct adaptive controller is designed to complete the global adaptive stability of the uncertain system. At the same time, the controller is also verified to possess the optimality. Example and simulations are provided to illustrate the effectiveness of the proposed method.展开更多
In this paper,an integrated estimation guidance and control(IEGC)system is designed based on the command filtered backstepping approach for circular field-of-view(FOV)strapdown missiles.The threedimensional integrated...In this paper,an integrated estimation guidance and control(IEGC)system is designed based on the command filtered backstepping approach for circular field-of-view(FOV)strapdown missiles.The threedimensional integrated estimation guidance and control nonlinear model with limited actuator deflection angle is established considering the seeker's FOV constraint.The boundary time-varying integral barrier Lyapunov function(IBLF)is employed in backstepping design to constrain the body line-of-sight(BLOS)in IEGC system to fit a circular FOV.Then,the nonlinear adaptive controller is designed to estimate the changing aerodynamic parameters.The generalized extended state observer(GESO)is designed to estimate the acceleration of the maneuvering targets and the unmatched time-varying disturbances for improving tracking accuracy.Furthermore,the command filters are used to solve the"differential expansion"problem during the backstepping design.The Lyapunov theory is used to prove the stability of the overall closed-loop IEGC system.Finally,the simulation results validate the integrated system's effectiveness,achieving high accuracy strikes against maneuvering targets.展开更多
Stability of a class of nonlinear systems with parametric uncertainty is dealt with. This kind of systems can be viewed as feedback interconnection systems. By constructing the Lyapunov function for one of the feedbac...Stability of a class of nonlinear systems with parametric uncertainty is dealt with. This kind of systems can be viewed as feedback interconnection systems. By constructing the Lyapunov function for one of the feedback interconnection systems, the Lyapunov function for this kind of systems is obtained. Sufficient conditions of global asymptotic stability for this class of systems are deduced. The simulation shows the effectiveness of the method.展开更多
Many industry processes can be described as Hammerstein-Wiener nonlinear systems. In this work, an improved constrained model predictive control algorithm is presented for Hammerstein-Wiener systems. In the new approa...Many industry processes can be described as Hammerstein-Wiener nonlinear systems. In this work, an improved constrained model predictive control algorithm is presented for Hammerstein-Wiener systems. In the new approach, the maximum and minimum of partial derivative for input and output nonlinearities are solved in the neighbourhood of the equilibrium. And several parameter-dependent Lyapunov functions, each one corresponding to a different vertex of polytopic descriptions models, are introduced to analyze the stability of Hammerstein-Wiener systems, but only one Lyapunov function is utilized to analyze system stability like the traditional method. Consequently, the conservation of the traditional quadratic stability is removed, and the terminal regions are enlarged. Simulation and field trial results show that the proposed algorithm is valid. It has higher control precision and shorter blowing time than the traditional approach.展开更多
The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic deriva...The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic derivatives of the Lyapunov functions, a theorem for asymptotic properties of the LaSal e-type described by limit sets of the solutions of the equations is obtained. Based on the asymptotic properties to the limit set, a theorem of asymptotic stability of the stochastic functional differential equations is also established, which enables us to construct the Lyapunov functions more easily in application. Particularly, the wel-known classical theorem on stochastic stability is a special case of our result, the operator LV is not required to be negative which is more general to fulfil and the stochastic perturbation plays an important role in it. These show clearly the improvement of the traditional method to find the Lyapunov functions. A numerical simulation example is given to il ustrate the usage of the method.展开更多
This article deals with the uniformly globally asymptotic controllability of discrete nonlinear systems with disturbances.It is shown that the system is uniformly globally asymptotic controllability with respect to a ...This article deals with the uniformly globally asymptotic controllability of discrete nonlinear systems with disturbances.It is shown that the system is uniformly globally asymptotic controllability with respect to a closed set if and only if there exists a smooth control Lyapunov function.Further, it is obtained that the control Lyapunov function may be used to construct a feedback law to stabilize the closed-loop system.In addition, it is proved that for periodic discrete systems, the resulted control Lyapunov functions are also time periodic.展开更多
The bursty events of available bit rate (ABR) traffic challenge the research on flow control algorithm. This bursty nature makes the network difficult to guarantee some performance such as decreasing cell loss especia...The bursty events of available bit rate (ABR) traffic challenge the research on flow control algorithm. This bursty nature makes the network difficult to guarantee some performance such as decreasing cell loss especially when congestion appears. In addition the robust stability analysis in the presence of virtual connections (VCs) variation is another inherent problem of the current rate-based algorithm. An explicit rate-based scheme is concerned. Some mathematical methods are adopted to minimize overshoot in the buffer to eliminate the growing congestion quickly. Then in linear matrix inequality (LMI) forms via Lyapunov stability argument relating to robustness issues in the presence of time-varying VCs is purposed in linear matrix inequality. A set of numerical examples guarantees this choice of algorithm parameters is robust stability. The simulations further back up our results.展开更多
The problem of admissibility analysis and control synthesis of discrete-time switched linear singular （SLS） systems for arbitrary switching laws is solved. By using the switched Lyapunov function approach, some new ...The problem of admissibility analysis and control synthesis of discrete-time switched linear singular （SLS） systems for arbitrary switching laws is solved. By using the switched Lyapunov function approach, some new sufficient conditions under which the SLS system is admissible for arbitrary switching laws are derived in terms of linear matrix inequalities （LMIs）. Based on the admissibility results, control synthesis is then to design switched state feedback and static output feedback controllers, guaranteeing that the resulting closed-loop system is admissible. The presented results can be viewed as the extensions of previous works on switched Lyapunov function approach from the regular switched systems to singular switched cases. Examples are provided to demonstrate the reduced conservatism and effectiveness of the proposed conditions.展开更多
To solve the seam tracking problem of mobile welding robot,a new controller based on the dynamics of mobile welding robot was designed using the method of backstepping kinematics into dynamics.A self-turning fuzzy con...To solve the seam tracking problem of mobile welding robot,a new controller based on the dynamics of mobile welding robot was designed using the method of backstepping kinematics into dynamics.A self-turning fuzzy controller and a fuzzy-Gaussian neural network(FGNN) controller were designed to complete coordinately controlling of cross-slider and wheels.The fuzzy-neural control algorithm was described by applying the Gaussian function and back propagation(BP) learning rule was used to tune the membership function in real time by applying the FGNN controller.To make the tracking more quickly and smoothly,the neural network controller based on dynamic model was designed,which utilized self-learning and self-adaptive ability of the neural network to deal with the partial uncertainty and the disturbances of the parameters of the robot dynamic model and real-time compensate the dynamics coupling.The results show that the selected control input torques make the system globally and asymptotically stable based on the Lyapunov function selected out;the accuracy of the proposed controller tracing is within ±0.4 mm and can satisfy the requirements of practical welding project.展开更多
This paper is concerned with the reliable H∞filtering,reliable filtering,Lyapunov function,sensor failure,linear matrix inequality(LMI)filtering problem against sensor failures for a class of discrete-time systems wi...This paper is concerned with the reliable H∞filtering,reliable filtering,Lyapunov function,sensor failure,linear matrix inequality(LMI)filtering problem against sensor failures for a class of discrete-time systems with sector-bounded nonlinearities.The resulting design is that the filtering error system is asymptotically stable and meets the prescribed H∞filtering,reliable filtering,Lyapunov function,sensor failure,linear matrix inequality(LMI)norm constraint in normal case as well as in sensor failure case.Sufficient conditions for the existence of the filter are obtained by using appropriate Lyapunov functional and linear matrix inequality(LMI)techniques.Moreover,in order to reduce the design conservativeness and get better performance,we adopt the slack variable method to realize the decoupling between the Lyapunov matrices and the system dynamic matrices.A numerical example is provided to demonstrate the effectiveness of the proposed designs.展开更多
In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in ...In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in control theory. As a result, many criteria for testing the stability of linear time-delay systems have been proposed. Significant progress has been made in the theory of impulsive systems and impulsive delay systems in recent years. However, the corresponding theory for uncertain impulsive systems and uncertain impulsive delay systems has not been fully developed. In this paper, robust stability criteria are established for uncertain linear delay impulsive systems by using Lyapunov function, Razumikhin techniques and the results obtained. Some examples are given to illustrate our theory.展开更多
The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed. The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed. ...The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed. The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed. Based on the optimization theory, a sufficient condition for convergence of this algorithm with bounded price estimation error is obtained. Furthermore, even when this sufficient condition doesn＇t hold, this algorithm can also converge, provided a modified step size, and an attraction region is obtained. Based on Lasalle＇s invariance principle applied to a suitable Lyapunov function, the dynamic system described by this algorithm is proved to be global stability if the error is zero. And the Newton-Like algorithm with bounded price estimation error is also globally stable if the error satisfies the sufficient condition for convergence. All trajectories ultimately converge to the equilibrium point.展开更多
基金Supported by Natural Science Foundation of Zhejiang Province P. R. China (Y105141)Natural Science Foundation of Fujian Province P.R.China (A0510025)Technological Project of Zhejiang Education Department,P. R. China(20050291)
文摘The construction of control Lyapunov functions for a class of nonlinear systems is considered. We develop a method by which a control Lyapunov function for the feedback linearizable part can be constructed systematically via Lyapunov equation. Moreover, by a control Lyapunov function of the feedback linearizable part and a Lyapunov function of the zero dynamics, a control Lyapunov function for the overall nonlinear system is established.
基金the Natural Science Foundation of Zhejiang Province,China (Y105141)Technological Project of Zhejiang Education Department,China (20050291).
文摘A method is developed by which control Lyapunov functions of a class of nonlinear systems can be constructed systematically. Based on the control Lyapunov function, a feedback control is obtained to stabilize the closed-loop system. In addition, this method is applied to stabilize the Benchmark system. A simulation shows the effectiveness of the method.
基金the Natural Science Foundation of China (60774011)the Natural ScienceFoundation of Zhejiang Province in China (Y105141)
文摘The stabilization of discrete nonlinear systems is studied. Based on control Lyapunov functions, a sufficient and necessary condition for a quadratic function to be a control Lyapunov function is given. From this condition, a continuous state feedback law is constructed explicitly. It can globally asymptotically stabilize the equilibrium of the closed-loop system. A simulation example shows the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China (6090405161021002)
文摘The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality （LMI） conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances.
文摘The problem of robust L 1 filtering with pole constraint in a disk for linear continuous polytopic uncertain systems is discussed. The attention is focused on design a linear asymptotically stable filter such that the filtering error system remains robustly stable, and has a L 1 performance constraint and pole constraint in a disk. The new robust L 1 performance criteria and regional pole placement condition are obtained via parameter-dependent Lyapunov functions method. Upon the proposed multiobjective performance criteria and by means of LMI technique, both full-order and reduced-order robust L 1 filter with suitable dynamic behavior can be obtained from the solution of convex optimization problems. Compared with earlier result in the quadratic framework, this approach turns out to be less conservative. The efficiency of the proposed technique is demonstrated by a numerical example.
文摘The thermal power boiler-turbine system is a complex system with high nonlinearity,time-delay and strong coupling.It is difi cult to obtain an excellent dynamic response by means of traditional PI/PID control when the power system load changes in a wide range.So far many advanced control strategies have been presented to solve the above problem,but most of these strategies are dependent on an accurate object model.
基金the National Natural Science Foundation of China(Grant Nos.62303380,62176214,62101590,62003268)the Aeronautical Science Foundation of China(Grant No.201907053001).
文摘This research focuses on detecting faults in flight vehicles with unstable subsystems operating asynchronously.By accounting for asynchronous switching,a switched model is established,and filters for fault detection(FD)in unstable subsystems are developed.The FD challenge is then transformed into an H∞filtering issue.Utilizing the multiple discontinuous Lyapunov function(MDLF)approach and the mode-dependent average dwell time(MDADT)method,sufficient conditions are derived to ensure stability during both fast and slow switching.Furthermore,the existence and solutions for FD filters are provided through linear matrix inequalities(LMIs).The simulation outcomes demonstrated the excellent performance of the developed method in studied cases.
文摘The problem of adaptive stabilization of a class of multi-input nonlinear systems with unknown parameters both in the state vector-field and the input vector-field has been considered. By employing the control Lyapunov function method, a direct adaptive controller is designed to complete the global adaptive stability of the uncertain system. At the same time, the controller is also verified to possess the optimality. Example and simulations are provided to illustrate the effectiveness of the proposed method.
文摘In this paper,an integrated estimation guidance and control(IEGC)system is designed based on the command filtered backstepping approach for circular field-of-view(FOV)strapdown missiles.The threedimensional integrated estimation guidance and control nonlinear model with limited actuator deflection angle is established considering the seeker's FOV constraint.The boundary time-varying integral barrier Lyapunov function(IBLF)is employed in backstepping design to constrain the body line-of-sight(BLOS)in IEGC system to fit a circular FOV.Then,the nonlinear adaptive controller is designed to estimate the changing aerodynamic parameters.The generalized extended state observer(GESO)is designed to estimate the acceleration of the maneuvering targets and the unmatched time-varying disturbances for improving tracking accuracy.Furthermore,the command filters are used to solve the"differential expansion"problem during the backstepping design.The Lyapunov theory is used to prove the stability of the overall closed-loop IEGC system.Finally,the simulation results validate the integrated system's effectiveness,achieving high accuracy strikes against maneuvering targets.
基金supported by the National Natural Science Foundation of China (60774011)the Natural Science Foundation of Zhejiang Province (Y105141)
文摘Stability of a class of nonlinear systems with parametric uncertainty is dealt with. This kind of systems can be viewed as feedback interconnection systems. By constructing the Lyapunov function for one of the feedback interconnection systems, the Lyapunov function for this kind of systems is obtained. Sufficient conditions of global asymptotic stability for this class of systems are deduced. The simulation shows the effectiveness of the method.
基金Project(61074074) supported by the National Natural Science Foundation,ChinaProject(KT2012C01J0401) supported by the Group Innovative Fund,China
文摘Many industry processes can be described as Hammerstein-Wiener nonlinear systems. In this work, an improved constrained model predictive control algorithm is presented for Hammerstein-Wiener systems. In the new approach, the maximum and minimum of partial derivative for input and output nonlinearities are solved in the neighbourhood of the equilibrium. And several parameter-dependent Lyapunov functions, each one corresponding to a different vertex of polytopic descriptions models, are introduced to analyze the stability of Hammerstein-Wiener systems, but only one Lyapunov function is utilized to analyze system stability like the traditional method. Consequently, the conservation of the traditional quadratic stability is removed, and the terminal regions are enlarged. Simulation and field trial results show that the proposed algorithm is valid. It has higher control precision and shorter blowing time than the traditional approach.
基金supported by the National Natural Science Foundation of China(61273126)the Natural Science Foundation of Guangdong Province(10251064101000008+1 种基金S201210009675)the Fundamental Research Funds for the Central Universities(2012ZM0059)
文摘The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic derivatives of the Lyapunov functions, a theorem for asymptotic properties of the LaSal e-type described by limit sets of the solutions of the equations is obtained. Based on the asymptotic properties to the limit set, a theorem of asymptotic stability of the stochastic functional differential equations is also established, which enables us to construct the Lyapunov functions more easily in application. Particularly, the wel-known classical theorem on stochastic stability is a special case of our result, the operator LV is not required to be negative which is more general to fulfil and the stochastic perturbation plays an important role in it. These show clearly the improvement of the traditional method to find the Lyapunov functions. A numerical simulation example is given to il ustrate the usage of the method.
基金supported by the National Natural Science Foundation of China (60774011)the Natural Science Foundation of Fujian Province (2008J0026)
文摘This article deals with the uniformly globally asymptotic controllability of discrete nonlinear systems with disturbances.It is shown that the system is uniformly globally asymptotic controllability with respect to a closed set if and only if there exists a smooth control Lyapunov function.Further, it is obtained that the control Lyapunov function may be used to construct a feedback law to stabilize the closed-loop system.In addition, it is proved that for periodic discrete systems, the resulted control Lyapunov functions are also time periodic.
文摘The bursty events of available bit rate (ABR) traffic challenge the research on flow control algorithm. This bursty nature makes the network difficult to guarantee some performance such as decreasing cell loss especially when congestion appears. In addition the robust stability analysis in the presence of virtual connections (VCs) variation is another inherent problem of the current rate-based algorithm. An explicit rate-based scheme is concerned. Some mathematical methods are adopted to minimize overshoot in the buffer to eliminate the growing congestion quickly. Then in linear matrix inequality (LMI) forms via Lyapunov stability argument relating to robustness issues in the presence of time-varying VCs is purposed in linear matrix inequality. A set of numerical examples guarantees this choice of algorithm parameters is robust stability. The simulations further back up our results.
基金Supported by the State Key Program of National Natural Science of China （60534010）, National Basic Research Program of China （973 Program）（2009CB320604）, National Natural Science Foundation of China （60674021）, the Funds for Creative Research Groups of China （60521003）, the 111 Project（B08015）, and the Funds of Ph.D. Program of Ministry of Eduction, China （20060145019）.
基金supported partly by the National Natural Science Foundation of China(6057400660835001)+1 种基金the Key Project of Chinese Ministry of Education(108060)the Jiangsu Planned Projects for Postdoctoral Research Funds(0802010c).
文摘The problem of admissibility analysis and control synthesis of discrete-time switched linear singular （SLS） systems for arbitrary switching laws is solved. By using the switched Lyapunov function approach, some new sufficient conditions under which the SLS system is admissible for arbitrary switching laws are derived in terms of linear matrix inequalities （LMIs）. Based on the admissibility results, control synthesis is then to design switched state feedback and static output feedback controllers, guaranteeing that the resulting closed-loop system is admissible. The presented results can be viewed as the extensions of previous works on switched Lyapunov function approach from the regular switched systems to singular switched cases. Examples are provided to demonstrate the reduced conservatism and effectiveness of the proposed conditions.
基金Project(2007309) supported by the Scientific Research Project of Hebei Provincial Education Office,ChinaProject(2007AA04Z209) supported by the National High-Tech Research and Development Program of China
文摘To solve the seam tracking problem of mobile welding robot,a new controller based on the dynamics of mobile welding robot was designed using the method of backstepping kinematics into dynamics.A self-turning fuzzy controller and a fuzzy-Gaussian neural network(FGNN) controller were designed to complete coordinately controlling of cross-slider and wheels.The fuzzy-neural control algorithm was described by applying the Gaussian function and back propagation(BP) learning rule was used to tune the membership function in real time by applying the FGNN controller.To make the tracking more quickly and smoothly,the neural network controller based on dynamic model was designed,which utilized self-learning and self-adaptive ability of the neural network to deal with the partial uncertainty and the disturbances of the parameters of the robot dynamic model and real-time compensate the dynamics coupling.The results show that the selected control input torques make the system globally and asymptotically stable based on the Lyapunov function selected out;the accuracy of the proposed controller tracing is within ±0.4 mm and can satisfy the requirements of practical welding project.
基金Supported by National Basic Research Program of China(973 Program)(2009CB320604)State Key Program of National Natural Science Foundation of China(60534010)+3 种基金National Natural Science Foundation of China(60674021)Funds for Creative Research Groups of China(60821063)the 111 Project(B08015)the Funds of Doctoral Program of Ministry of Education of China(20060145019)
文摘This paper is concerned with the reliable H∞filtering,reliable filtering,Lyapunov function,sensor failure,linear matrix inequality(LMI)filtering problem against sensor failures for a class of discrete-time systems with sector-bounded nonlinearities.The resulting design is that the filtering error system is asymptotically stable and meets the prescribed H∞filtering,reliable filtering,Lyapunov function,sensor failure,linear matrix inequality(LMI)norm constraint in normal case as well as in sensor failure case.Sufficient conditions for the existence of the filter are obtained by using appropriate Lyapunov functional and linear matrix inequality(LMI)techniques.Moreover,in order to reduce the design conservativeness and get better performance,we adopt the slack variable method to realize the decoupling between the Lyapunov matrices and the system dynamic matrices.A numerical example is provided to demonstrate the effectiveness of the proposed designs.
基金This project was supported by the National Natural Science Foundation of China (60274007) NSERC-Canada.
文摘In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in control theory. As a result, many criteria for testing the stability of linear time-delay systems have been proposed. Significant progress has been made in the theory of impulsive systems and impulsive delay systems in recent years. However, the corresponding theory for uncertain impulsive systems and uncertain impulsive delay systems has not been fully developed. In this paper, robust stability criteria are established for uncertain linear delay impulsive systems by using Lyapunov function, Razumikhin techniques and the results obtained. Some examples are given to illustrate our theory.
基金supported in part by the National Outstanding Youth Foundation of P.R.China (60525303)the National Natural Science Foundation of P.R.China(60404022,60604004)+2 种基金the Natural Science Foundation of Hebei Province (102160)the special projects in mathematics funded by the Natural Science Foundation of Hebei Province(07M005)the NS of Education Office in Hebei Province (2004123).
文摘The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed. The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed. Based on the optimization theory, a sufficient condition for convergence of this algorithm with bounded price estimation error is obtained. Furthermore, even when this sufficient condition doesn＇t hold, this algorithm can also converge, provided a modified step size, and an attraction region is obtained. Based on Lasalle＇s invariance principle applied to a suitable Lyapunov function, the dynamic system described by this algorithm is proved to be global stability if the error is zero. And the Newton-Like algorithm with bounded price estimation error is also globally stable if the error satisfies the sufficient condition for convergence. All trajectories ultimately converge to the equilibrium point.
