Signal filtering and differential acquisition are classic yet challenging issues in control engineering.The discrete-time optimal control(DTOC)based on classic tracking differentiator(TD)can effectively extract differ...Signal filtering and differential acquisition are classic yet challenging issues in control engineering.The discrete-time optimal control(DTOC)based on classic tracking differentiator(TD)can effectively extract differentiation signals and filter signals,while eliminating the chattering problem that arises during the discretization of the continuous solution.However,under external disturbance,the convergence mode may change,leading to overshoot and noise amplification.In this paper,a dual-switching strategy is proposed,which can alternate between the base double-integral system and its dual system according to the quadrant of the system’s state.And a novel linearized control law is also introduced,deriving a novel dual-switch tracking differentiator.Further analysis of system convergence and time optimality is provided.Simulation results show that the application of this dual-switching strategy notably reduces overshoot in both tracking and differential signals while enhancing noise filtering performance.Moreover,experiments conducted on a permanent magnet synchronous motor(PMSM)platform,where the proposed TD acts as a filter in the speed feedback loop,demonstrate that the standard deviation between the reference speed and the target speed(at a constant speed of 378 r/min)decreased from 5.63 r/min to 4.93 r/min,compared to the moving average algorithm.展开更多
The path-following control of the asymmetry underactuated unmanned surface vehicle(USV) under external disturbances such as unknown constant and irrational ocean currents is discussed, and an adaptive sliding-mode pat...The path-following control of the asymmetry underactuated unmanned surface vehicle(USV) under external disturbances such as unknown constant and irrational ocean currents is discussed, and an adaptive sliding-mode path-following control system is proposed, which comprises a path-variable updated law,a modified integral line-of-sight(ILOS) guidance law based on a time-varying lookahead distance and adaptive feedback linearizing controllers combined with sliding-mode technique. A more accurate USV model without the assumption of having diagonal inertia and damping matrices is first presented, aiming at improving the performance of the path-following control. Next, the coordinate transformation is adopted to decouple the sway dynamic from the rudder angle, and the path-following errors dynamics without non-singular problem are presented in the moving Frenet-Serret frame. Then, based on the cascaded theorem and the adaptive sliding-mode method, the adaptive control law of position errors and course error are designed, among which the lookahead distance and integral gain are all computed as different functions of cross-track error to estimate and compensate the sideslip angle caused by external disturbances adaptively. Finally, according to the Lyapunov and cascaded theorem, the control system proposed is proved to be uniform globally asymptotic stability(UGAS) and uniform semiglobal exponential stability(USGES) when the control objectives are all achieved. Simulation results illustrate the precision and high-quality performance of this new controller.展开更多
This work focuses on motion control of high-velocity autonomous underwater vehicle(AUV).Conventional methods are effective solutions to motion control of low-and-medium-velocity AUV.Usually not taken into consideratio...This work focuses on motion control of high-velocity autonomous underwater vehicle(AUV).Conventional methods are effective solutions to motion control of low-and-medium-velocity AUV.Usually not taken into consideration in the control model,the residual dead load and damping force which vary with the AUV’s velocity tend to result in difficulties in motion control or even failure in convergence in the case of high-velocity movement.With full consideration given to the influence of residual dead load and changing damping force upon AUV motion control,a novel sliding-mode controller(SMC)is proposed in this work.The stability analysis of the proposed controller is carried out on the basis of Lyapunov function.The sea trials results proved the superiority of the sliding-mode controller over sigmoid-function-based controller(SFC).The novel controller demonstrated its effectiveness by achieving admirable control results in the case of high-velocity movement.展开更多
This paper investigates the overload stabilization problem of the rolling-missile subject to parameters uncertainty and actuator saturation. In order to solve this problem, a sliding-mode control(SMC) scheme is techni...This paper investigates the overload stabilization problem of the rolling-missile subject to parameters uncertainty and actuator saturation. In order to solve this problem, a sliding-mode control(SMC) scheme is technically employed by using the backstepping approach to make the dynamic system stable. In addition,SMC with the tanh-type switching function plays an important role in reducing intrinsic vibration. Furthermore, an auxiliary system(AS) is developed to compensate for nonlinear terms arising from input saturation. Finally, the simulation results provide a solution to demonstrate that the suggested SMC and the AS methodology have advantages of strong tracking capability, anti-interference ability and anti-saturation performance.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 robust H∞ control problem of norm bounded uncertain discrete Takagi-Sugeno （T-S） fuzzy systems with state delay is addressed. First, by constructing an appropriate basis-dependent Lyapunov-Krasovskii function, ...The robust H∞ control problem of norm bounded uncertain discrete Takagi-Sugeno （T-S） fuzzy systems with state delay is addressed. First, by constructing an appropriate basis-dependent Lyapunov-Krasovskii function, a new delay-dependent sufficient condition on robust H∞-disturbance attenuation is presented, in which both robust stability and prescribed H∞ performance are guaranteed to be achieved. Then based on the condition, a delay-dependent robust Hoo controller design scheme is developed in term of a convex algorithm. Finally, examples are given to illustrate the effectiveness of the proposed method.展开更多
A nonlinear robust control strategy is proposed to force an underactuated surface ship to follow a predefined path with uncertain environmental disturbance and parameters.In the controller design,a high-gain observer ...A nonlinear robust control strategy is proposed to force an underactuated surface ship to follow a predefined path with uncertain environmental disturbance and parameters.In the controller design,a high-gain observer is used to estimate velocities,thus only position and yaw angle measurements are required.The control problem of underactuated system is transformed into a control of fully actuated system through adopting an improved line-of-sight(LOS) guidance law.A sliding-mode controller is designed to eliminate the yaw angle error,and provide the control system robustness.The control law is proved semi-globally exponentially stable(SGES) by applying Lyapunov stability theory,and numerical simulation using real data of a monohull ship illustrates the effectiveness and robustness of the proposed methodology.展开更多
This paper focuses on the problem of non-fragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems（DFBS）.Based on the parallel distributed compensation（PDC） approach,the sufficient co...This paper focuses on the problem of non-fragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems（DFBS）.Based on the parallel distributed compensation（PDC） approach,the sufficient conditions are derived such that the closed-loop system is asymptotically stable and the cost function value is no more than a certain upper bound in the presence of the additive controller gain perturbations.The non-fragile guaranteed cost controller can be obtained by solving a set of bilinear matrix inequalities（BMIs）.The Van de Vusse model is utilized to demonstrate the validity and effectiveness of the proposed approach.展开更多
The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are de...The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are derived to guarantee the stability of the overall fuzzy system. The stabilization conditions are further formulated into linear matrix inequality （LMI） so that the desired controller can be easily obtained by using the Matlab LMI toolbox. In comparison with the existing results, the drawbacks, such as coordinate transformation, same output matrices, have been elim- inated. Finally, a simulation example shows that the approach is effective.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 robust reliable H∞ control problem for discrete-time Markovian jump systems with actuator failures is studied. A more practical model of actuator failures than outage is considered. Based on the state feedback me...The robust reliable H∞ control problem for discrete-time Markovian jump systems with actuator failures is studied. A more practical model of actuator failures than outage is considered. Based on the state feedback method, the resulting closed-loop systems are reliable in that they remain robust stochastically stable and satisfy a certain level of H∞ disturbance attenuation not only when all actuators are operational, but also in case of some actuator failures, The solvability condition of controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities （LMIs）. A numerical example is also given to illustrate the design procedures and their effectiveness.展开更多
A quite great progress of the supervisory control theory for discrete event systems (DES)has been made in the past nearly twenty years, and now, automata, formal language and Petri nets become the main research tools....A quite great progress of the supervisory control theory for discrete event systems (DES)has been made in the past nearly twenty years, and now, automata, formal language and Petri nets become the main research tools. This paper focus on the Petri nets based supervisory control theory of DES. Firstly, we review the research results in this field, and claim that there generally exists a problem in Petri nets based supervisory control theory of DES, that is, the deadlock caused by the controller introduced to enforce the given specification occurs in the closed-loop systems, especially the deadlock occurs in the closed-loop system in which the original plant is live. Finally, a possible research direction is presented for the solution of this problem.展开更多
An indirect adaptive fuzzy control scheme is developed for a class of nonlinear discrete-time systems. In this method, two fuzzy logic systems are used to approximate the unknown functions, and the parameters of membe...An indirect adaptive fuzzy control scheme is developed for a class of nonlinear discrete-time systems. In this method, two fuzzy logic systems are used to approximate the unknown functions, and the parameters of membership functions in fuzzy logic systems are adjusted according to adaptive laws for the purpose of controlling the plant to track a reference trajectory. It is proved that the scheme can not only guarantee the boundedness of the input and output of the closed-loop system, but also make the tracking error converge to a small neighborhood of the origin. Simulation results indicate the effectiveness of this scheme.展开更多
The memory state feedback control problem for a class of discrete-time systems with input delay and unknown state delay is addressed based on LMIs and Lyapunov-Krasovskii functional method. Under the action of our des...The memory state feedback control problem for a class of discrete-time systems with input delay and unknown state delay is addressed based on LMIs and Lyapunov-Krasovskii functional method. Under the action of our designed adaptive control law, the unknown time-delay parameter is included in memory state feedback controller. Using LMI technique, delay-dependent sufficient conditions for the existence of the feedback controller are obtained. Finally, the effectiveness of the proposed design method is demonstrated by a numerical example.展开更多
A fuzzy sliding-mode control (FSMC) scheme based on T-S fuzzy models was proposed for the permanent magnet synchronous motor (PMSM) drive system to solve the speed tracking problem. A T-S fuzzy model was firstly forme...A fuzzy sliding-mode control (FSMC) scheme based on T-S fuzzy models was proposed for the permanent magnet synchronous motor (PMSM) drive system to solve the speed tracking problem. A T-S fuzzy model was firstly formed to represent the nonlinear system of PMSM. For converting the tracking control into a stabilization problem, a new control design was proposed to define the internal desired states. Then, the FSMC controller for PMSM system with parameter variation and load disturbance was designed based on the fuzzy model. The performance of the proposed controller was verified by experimental results on PMSM system. The results show that the FSMC scheme can drive the dynamics of PMSM into a designated sliding surface in finite time and guarantee the property of asymptotical stability. The information of upper bound of modeling errors as well as perturbations is not required when using the FSMC controller.展开更多
One of the first attempts to derive energy-to-peak performance criteria and state-feedback controller design problem for linear parameter-varying discrete time systems with time delay is provided. Firstly, we present ...One of the first attempts to derive energy-to-peak performance criteria and state-feedback controller design problem for linear parameter-varying discrete time systems with time delay is provided. Firstly, we present a parameter-dependent l 2-l ∞ performance criterion using a parameter-dependent Lyapunov function. Upon the conditions addressed, an improved parameter-dependent l 2-l ∞ performance criterion is established by the introduction of a slack variable, which exhibits a kind of decoupling between Lyapunov functions and system matrices. This kind of decoupling enables us to obtain more easily tractable conditions for analysis and synthesis problems. Then, the corresponding parameter-dependent state-feedback controller design is investigated upon these performance criteria, with sufficient conditions obtained for the existence of admissible controllers in terms of parameterized linear matrix inequalities. Finally, a numerical example is provided to illustrate the feasibility and advantage of the proposed controller design procedure.展开更多
A discrete observer-based repetitive control(RC) design method for a linear system with uncertainties was presented based on two-dimensional(2D) system theory. Firstly, a 2D discrete model was established to describe ...A discrete observer-based repetitive control(RC) design method for a linear system with uncertainties was presented based on two-dimensional(2D) system theory. Firstly, a 2D discrete model was established to describe both the control behavior within a repetition period and the learning process taking place between periods. Next, by converting the designing problem of repetitive controller into one of the feedback gains of reconstructed variables, the stable condition was obtained through linear matrix inequality(LMI) and also the gain coefficient of repetitive system. Numerical simulation shows an exceptional feasibility of this proposal with remarkable robustness and tracking speed.展开更多
基金Project(QZKFKT2023-012)supported by the State Key Laboratory of Heavy-duty and Express High-power Electric Locomotive,China。
文摘Signal filtering and differential acquisition are classic yet challenging issues in control engineering.The discrete-time optimal control(DTOC)based on classic tracking differentiator(TD)can effectively extract differentiation signals and filter signals,while eliminating the chattering problem that arises during the discretization of the continuous solution.However,under external disturbance,the convergence mode may change,leading to overshoot and noise amplification.In this paper,a dual-switching strategy is proposed,which can alternate between the base double-integral system and its dual system according to the quadrant of the system’s state.And a novel linearized control law is also introduced,deriving a novel dual-switch tracking differentiator.Further analysis of system convergence and time optimality is provided.Simulation results show that the application of this dual-switching strategy notably reduces overshoot in both tracking and differential signals while enhancing noise filtering performance.Moreover,experiments conducted on a permanent magnet synchronous motor(PMSM)platform,where the proposed TD acts as a filter in the speed feedback loop,demonstrate that the standard deviation between the reference speed and the target speed(at a constant speed of 378 r/min)decreased from 5.63 r/min to 4.93 r/min,compared to the moving average algorithm.
基金supported by the National Social Science Foundation of China(15GJ003-278)the National Natural Science Foundation of China(71501182)
文摘The path-following control of the asymmetry underactuated unmanned surface vehicle(USV) under external disturbances such as unknown constant and irrational ocean currents is discussed, and an adaptive sliding-mode path-following control system is proposed, which comprises a path-variable updated law,a modified integral line-of-sight(ILOS) guidance law based on a time-varying lookahead distance and adaptive feedback linearizing controllers combined with sliding-mode technique. A more accurate USV model without the assumption of having diagonal inertia and damping matrices is first presented, aiming at improving the performance of the path-following control. Next, the coordinate transformation is adopted to decouple the sway dynamic from the rudder angle, and the path-following errors dynamics without non-singular problem are presented in the moving Frenet-Serret frame. Then, based on the cascaded theorem and the adaptive sliding-mode method, the adaptive control law of position errors and course error are designed, among which the lookahead distance and integral gain are all computed as different functions of cross-track error to estimate and compensate the sideslip angle caused by external disturbances adaptively. Finally, according to the Lyapunov and cascaded theorem, the control system proposed is proved to be uniform globally asymptotic stability(UGAS) and uniform semiglobal exponential stability(USGES) when the control objectives are all achieved. Simulation results illustrate the precision and high-quality performance of this new controller.
基金Project(2011AA09A106)supported by the Hi-tech Research and Development Program of ChinaProjects(51179035,51779057)supported by the National Natural Science Foundation of ChinaProject(2015ZX01041101)supported by Major National Science and Technology of China
文摘This work focuses on motion control of high-velocity autonomous underwater vehicle(AUV).Conventional methods are effective solutions to motion control of low-and-medium-velocity AUV.Usually not taken into consideration in the control model,the residual dead load and damping force which vary with the AUV’s velocity tend to result in difficulties in motion control or even failure in convergence in the case of high-velocity movement.With full consideration given to the influence of residual dead load and changing damping force upon AUV motion control,a novel sliding-mode controller(SMC)is proposed in this work.The stability analysis of the proposed controller is carried out on the basis of Lyapunov function.The sea trials results proved the superiority of the sliding-mode controller over sigmoid-function-based controller(SFC).The novel controller demonstrated its effectiveness by achieving admirable control results in the case of high-velocity movement.
基金supported by the Fundamental Research Funds for the Central Universities (30919011401)。
文摘This paper investigates the overload stabilization problem of the rolling-missile subject to parameters uncertainty and actuator saturation. In order to solve this problem, a sliding-mode control(SMC) scheme is technically employed by using the backstepping approach to make the dynamic system stable. In addition,SMC with the tanh-type switching function plays an important role in reducing intrinsic vibration. Furthermore, an auxiliary system(AS) is developed to compensate for nonlinear terms arising from input saturation. Finally, the simulation results provide a solution to demonstrate that the suggested SMC and the AS methodology have advantages of strong tracking capability, anti-interference ability and anti-saturation performance.
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.
文摘The robust H∞ control problem of norm bounded uncertain discrete Takagi-Sugeno （T-S） fuzzy systems with state delay is addressed. First, by constructing an appropriate basis-dependent Lyapunov-Krasovskii function, a new delay-dependent sufficient condition on robust H∞-disturbance attenuation is presented, in which both robust stability and prescribed H∞ performance are guaranteed to be achieved. Then based on the condition, a delay-dependent robust Hoo controller design scheme is developed in term of a convex algorithm. Finally, examples are given to illustrate the effectiveness of the proposed method.
基金Projects(61004008,51509055)supported by the National Natural Science Foundation of ChinaProject(61422230302162223013)supported by the Laboratory of Science and Technology on Water Jet Propulsion,China
文摘A nonlinear robust control strategy is proposed to force an underactuated surface ship to follow a predefined path with uncertain environmental disturbance and parameters.In the controller design,a high-gain observer is used to estimate velocities,thus only position and yaw angle measurements are required.The control problem of underactuated system is transformed into a control of fully actuated system through adopting an improved line-of-sight(LOS) guidance law.A sliding-mode controller is designed to eliminate the yaw angle error,and provide the control system robustness.The control law is proved semi-globally exponentially stable(SGES) by applying Lyapunov stability theory,and numerical simulation using real data of a monohull ship illustrates the effectiveness and robustness of the proposed methodology.
基金supported by the National Natural Science Foundation of China(60374015)
文摘This paper focuses on the problem of non-fragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems（DFBS）.Based on the parallel distributed compensation（PDC） approach,the sufficient conditions are derived such that the closed-loop system is asymptotically stable and the cost function value is no more than a certain upper bound in the presence of the additive controller gain perturbations.The non-fragile guaranteed cost controller can be obtained by solving a set of bilinear matrix inequalities（BMIs）.The Van de Vusse model is utilized to demonstrate the validity and effectiveness of the proposed approach.
文摘The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are derived to guarantee the stability of the overall fuzzy system. The stabilization conditions are further formulated into linear matrix inequality （LMI） so that the desired controller can be easily obtained by using the Matlab LMI toolbox. In comparison with the existing results, the drawbacks, such as coordinate transformation, same output matrices, have been elim- inated. Finally, a simulation example shows that the approach is effective.
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.
基金the National Natural Science Foundation of China (60574001)Program for New Century Excellent Talents in University (05-0485)Program for Innovative Research Team of Jiangnan University
文摘The robust reliable H∞ control problem for discrete-time Markovian jump systems with actuator failures is studied. A more practical model of actuator failures than outage is considered. Based on the state feedback method, the resulting closed-loop systems are reliable in that they remain robust stochastically stable and satisfy a certain level of H∞ disturbance attenuation not only when all actuators are operational, but also in case of some actuator failures, The solvability condition of controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities （LMIs）. A numerical example is also given to illustrate the design procedures and their effectiveness.
基金Supported in part by the National Outstanding Youth Science Foundation of P.R.China (60025308) Doctor Degree Program Foundation of P.R.China (20020335103), Scientific Research Program of Department of Education of Zhejiang Province, P.R.China (20040149)
文摘A quite great progress of the supervisory control theory for discrete event systems (DES)has been made in the past nearly twenty years, and now, automata, formal language and Petri nets become the main research tools. This paper focus on the Petri nets based supervisory control theory of DES. Firstly, we review the research results in this field, and claim that there generally exists a problem in Petri nets based supervisory control theory of DES, that is, the deadlock caused by the controller introduced to enforce the given specification occurs in the closed-loop systems, especially the deadlock occurs in the closed-loop system in which the original plant is live. Finally, a possible research direction is presented for the solution of this problem.
基金surported by Tianjin Science and Technology Development for Higher Education(20051206).
文摘An indirect adaptive fuzzy control scheme is developed for a class of nonlinear discrete-time systems. In this method, two fuzzy logic systems are used to approximate the unknown functions, and the parameters of membership functions in fuzzy logic systems are adjusted according to adaptive laws for the purpose of controlling the plant to track a reference trajectory. It is proved that the scheme can not only guarantee the boundedness of the input and output of the closed-loop system, but also make the tracking error converge to a small neighborhood of the origin. Simulation results indicate the effectiveness of this scheme.
基金supported by the National Natural Science Foundation of China (60574006 60804017+2 种基金 608350017)the Foundation of Doctor(20060286039)the Jiangsu Provincal Sustentation Fund of Recruiting Post Doctor(1660631171)
文摘The memory state feedback control problem for a class of discrete-time systems with input delay and unknown state delay is addressed based on LMIs and Lyapunov-Krasovskii functional method. Under the action of our designed adaptive control law, the unknown time-delay parameter is included in memory state feedback controller. Using LMI technique, delay-dependent sufficient conditions for the existence of the feedback controller are obtained. Finally, the effectiveness of the proposed design method is demonstrated by a numerical example.
基金Project (60835004) supported by the National Natural Science Foundation of China
文摘A fuzzy sliding-mode control (FSMC) scheme based on T-S fuzzy models was proposed for the permanent magnet synchronous motor (PMSM) drive system to solve the speed tracking problem. A T-S fuzzy model was firstly formed to represent the nonlinear system of PMSM. For converting the tracking control into a stabilization problem, a new control design was proposed to define the internal desired states. Then, the FSMC controller for PMSM system with parameter variation and load disturbance was designed based on the fuzzy model. The performance of the proposed controller was verified by experimental results on PMSM system. The results show that the FSMC scheme can drive the dynamics of PMSM into a designated sliding surface in finite time and guarantee the property of asymptotical stability. The information of upper bound of modeling errors as well as perturbations is not required when using the FSMC controller.
基金Supported-by Program for New Century Excellent Talents in Universities of China （NCET-05-0607）, National Natural Science Foundation of China （60774010）, and Program for Fundamental Research of Natural Sciences in Universities of Jiangsu Province （07KJB510114）
基金Supported by Program for New Century Excellent Talents in Universities of China （NCET-05-0607）, National Natural Science Foundation of China （60774010）, and Project for Fundamental Research of Natural Sciences in Universities of Jiangsu Province （07KJB510114）
文摘One of the first attempts to derive energy-to-peak performance criteria and state-feedback controller design problem for linear parameter-varying discrete time systems with time delay is provided. Firstly, we present a parameter-dependent l 2-l ∞ performance criterion using a parameter-dependent Lyapunov function. Upon the conditions addressed, an improved parameter-dependent l 2-l ∞ performance criterion is established by the introduction of a slack variable, which exhibits a kind of decoupling between Lyapunov functions and system matrices. This kind of decoupling enables us to obtain more easily tractable conditions for analysis and synthesis problems. Then, the corresponding parameter-dependent state-feedback controller design is investigated upon these performance criteria, with sufficient conditions obtained for the existence of admissible controllers in terms of parameterized linear matrix inequalities. Finally, a numerical example is provided to illustrate the feasibility and advantage of the proposed controller design procedure.
基金Project(61104072) supported by the National Natural Science Foundation of China
文摘A discrete observer-based repetitive control(RC) design method for a linear system with uncertainties was presented based on two-dimensional(2D) system theory. Firstly, a 2D discrete model was established to describe both the control behavior within a repetition period and the learning process taking place between periods. Next, by converting the designing problem of repetitive controller into one of the feedback gains of reconstructed variables, the stable condition was obtained through linear matrix inequality(LMI) and also the gain coefficient of repetitive system. Numerical simulation shows an exceptional feasibility of this proposal with remarkable robustness and tracking speed.
