As saturation is involved in the stabilizing feedback control of a linear discrete-time system, the original global-asymptotic stabilization (GAS) may drop to region-asymptotic stabilization (RAS). How to test if the ...As saturation is involved in the stabilizing feedback control of a linear discrete-time system, the original global-asymptotic stabilization (GAS) may drop to region-asymptotic stabilization (RAS). How to test if the saturated feedback system is GAS or RAS? The paper presents a criterion to answer this question, and describes an algorithm to calculate an invariant attractive ellipsoid for the RAS case. At last, the effectiveness of the approach is shown with examples.展开更多
This paper is concerned with the problem of robust sliding-mode filtering for a class of uncertain nonlinear discrete-time systems with time-delays. The nonlinearities are assumed to satisfy global Lipschitz condition...This paper is concerned with the problem of robust sliding-mode filtering for a class of uncertain nonlinear discrete-time systems with time-delays. The nonlinearities are assumed to satisfy global Lipschitz conditions and parameter uncertainties are supposed to reside in a polytope. The resulting filter is of the Luenberger type with the discontinuous form. A sufficient condition with delay-dependency is proposed for existence of such a filter. And the desired filter can be found by solving a set of matrix inequalities. The resulting filter adapts for the systems whose noise input is real functional bounded and not be required to be energy bounded. A numerical example is given to illustrate the effectiveness of the proposed design method.展开更多
The problem of fault detection for linear discrete timevarying systems with multiplicative noise is dealt with.By using an observer-based robust fault detection filter（FDF） as a residual generator,the design of the ...The problem of fault detection for linear discrete timevarying systems with multiplicative noise is dealt with.By using an observer-based robust fault detection filter（FDF） as a residual generator,the design of the FDF is formulated in the framework of H ∞ filtering for a class of stochastic time-varying systems.A sufficient condition for the existence of the FDF is derived in terms of a Riccati equation.The determination of the parameter matrices of the filter is converted into a quadratic optimization problem,and an analytical solution of the parameter matrices is obtained by solving the Riccati equation.Numerical examples are given to illustrate the effectiveness of the proposed method.展开更多
A robust stabilization problem is considered for time delay nonlinear discrete-time systems based on T-S fuzzy model. A necessary and sufficient condition for the existence of such controllers is given through Lyapuno...A robust stabilization problem is considered for time delay nonlinear discrete-time systems based on T-S fuzzy model. A necessary and sufficient condition for the existence of such controllers is given through Lyapunov stability theorem. And it is further shown that this condition is equivalent to the solvability of a certain linear matrix inequality, which can be solved easily by using the LMI toolbox of Matlab. At last, an illustrative example of truck-trailer is presented to show the feasibility and effectiveness of the proposed method.展开更多
The stability and stabilization of a class of nonlinear discrete time delayed systems(NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov–Krasovskii function...The stability and stabilization of a class of nonlinear discrete time delayed systems(NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov–Krasovskii functional method, a sufficient delaydependent condition for asymptotic stability of nonlinear systems is offered. Then, this condition is used to design a new efficient delayed state feedback controller(DSFC) for stabilization of such systems. These conditions are in the linear matrix inequality(LMI) framework. Illustrative examples confirm the improvement of the proposed approach over the similar cases. Furthermore, the obtained stability and stabilization conditions will be extended to uncertain discrete time delayed systems(UDTDS) with polytopic parameter uncertainties and also with norm-bounded parameter uncertainties.展开更多
This paper deals with the problem of the optimal fault detection (FD) for linear discrete time-varying (LDTV) systems with delayed state and l(2)-norm bounded unknown input. The novelty lies in the designing of an eva...This paper deals with the problem of the optimal fault detection (FD) for linear discrete time-varying (LDTV) systems with delayed state and l(2)-norm bounded unknown input. The novelty lies in the designing of an evaluation function for the robust FD. The basic idea is to directly construct an evaluation function by using a weighted l(2)-norm of the measurement output, which achieves an optimal trade-off between the sensitivity to fault and the robustness to l(2)-norm bounded unknown input. To avoid complex computation, a feasible solution is obtained via the recursive computation by applying the orthogonal projection. It is shown that such an evaluation function provides a unified scheme for both the cases of unknown input being l(2)-norm bounded and jointly normal distribution, while a threshold may be chosen based on a priori knowledge of unknown input. A numerical example is given to demonstrate the effectiveness of the proposed method.展开更多
This paper deals with the problem of optimal fault detection filter （FDF） design for a class of discrete-time switched linear systems under arbitrary switching. By using an observer-based FDF as a residual generator...This paper deals with the problem of optimal fault detection filter （FDF） design for a class of discrete-time switched linear systems under arbitrary switching. By using an observer-based FDF as a residual generator, the design of the FDF is formulated into an optimization problem through maximizing the H_/H∞ or H∞/H∞ performance index. With the aid of an operator optimization method, it is shown that a mode-dependent unified optimal solution can be derived by solving a coupled Riccati equation. A numerical example is given to show the effectiveness of the proposed method.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
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
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
The robust H∞ filtering problem for uncertain discrete-time Markovian jump linear systems with mode- dependent time-delays is investigated. Attention is focused on designing a Markovian jump linear filter that ensure...The robust H∞ filtering problem for uncertain discrete-time Markovian jump linear systems with mode- dependent time-delays is investigated. Attention is focused on designing a Markovian jump linear filter that ensures robust stochastic stability while achieving a prescribed H∞ performance level of the resulting filtering error system, for all admissible uncertainties. The key features of the approach include the introduction of a new type of stochastic Lyapunov functional and some free weighting matrix variables. Sufficient conditions for the solvability of this problem are obtained in terms of a set of linear matrix inequalities. Numerical examples are provided to demonstrate the reduced conservatism of the proposed approach.展开更多
This article deals with the robust stability analysis and passivity of uncertain discrete-time Takagi- Sugeno （T-S） fuzzy systems with time delays. The T-S fuzzy model with parametric uncertainties can approximate n...This article deals with the robust stability analysis and passivity of uncertain discrete-time Takagi- Sugeno （T-S） fuzzy systems with time delays. The T-S fuzzy model with parametric uncertainties can approximate nonlinear uncertain systems at any precision. A sufficient condition on the existence of robust passive controller is established based on the Lyapunov stability theory. With the help of linear matrix inequality （LMI） method, robust passive controllers are designed so that the closed-loop system is robust stable and strictly passive. Furthermore, a convex optimization problem with LMI constraints is formulated to design robust passive controllers with the maximum dissipation rate. A numerical example illustrates the validity of the proposed method.展开更多
A newly designed approach of simultaneous stabilization is given for linear discrete time-delay systems. The problem of stabilization for a collection of systems is discussed initially. Adequate condition are obtained...A newly designed approach of simultaneous stabilization is given for linear discrete time-delay systems. The problem of stabilization for a collection of systems is discussed initially. Adequate condition are obtained in terms of linear matrix inequalities （LMIs） which are independent of time delays such that the resultant collection of discrete time-delay systems are stable with an upper bound of the quadratic performance index. Subsequently, controllers are designed such that the resultant closed-loop discrete time-delay systems are simultaneously stabilized with the upper bound of the quadratic performance index. Finally,a numerical example is given to illustrate the design method.展开更多
基金Supported by National Natural Science Foundation of P. R. China (60174040)
文摘As saturation is involved in the stabilizing feedback control of a linear discrete-time system, the original global-asymptotic stabilization (GAS) may drop to region-asymptotic stabilization (RAS). How to test if the saturated feedback system is GAS or RAS? The paper presents a criterion to answer this question, and describes an algorithm to calculate an invariant attractive ellipsoid for the RAS case. At last, the effectiveness of the approach is shown with examples.
基金Supported by National Natural Science Foundation of P. R. China (69874008)
文摘This paper is concerned with the problem of robust sliding-mode filtering for a class of uncertain nonlinear discrete-time systems with time-delays. The nonlinearities are assumed to satisfy global Lipschitz conditions and parameter uncertainties are supposed to reside in a polytope. The resulting filter is of the Luenberger type with the discontinuous form. A sufficient condition with delay-dependency is proposed for existence of such a filter. And the desired filter can be found by solving a set of matrix inequalities. The resulting filter adapts for the systems whose noise input is real functional bounded and not be required to be energy bounded. A numerical example is given to illustrate the effectiveness of the proposed design method.
基金supported by the National Natural Science Foundation of China (61174121,61121003)the National High Technology Researchand Development Program of China (863 Program) (2008AA121302)+1 种基金the National Basic Research Program of China (973 Program)(2009CB724000)the Research Fund for the Doctoral Program of Higher Education of China
文摘The problem of fault detection for linear discrete timevarying systems with multiplicative noise is dealt with.By using an observer-based robust fault detection filter（FDF） as a residual generator,the design of the FDF is formulated in the framework of H ∞ filtering for a class of stochastic time-varying systems.A sufficient condition for the existence of the FDF is derived in terms of a Riccati equation.The determination of the parameter matrices of the filter is converted into a quadratic optimization problem,and an analytical solution of the parameter matrices is obtained by solving the Riccati equation.Numerical examples are given to illustrate the effectiveness of the proposed method.
基金Supported by National Natural Science Foundation of P. R. China (60274009)
文摘A robust stabilization problem is considered for time delay nonlinear discrete-time systems based on T-S fuzzy model. A necessary and sufficient condition for the existence of such controllers is given through Lyapunov stability theorem. And it is further shown that this condition is equivalent to the solvability of a certain linear matrix inequality, which can be solved easily by using the LMI toolbox of Matlab. At last, an illustrative example of truck-trailer is presented to show the feasibility and effectiveness of the proposed method.
文摘The stability and stabilization of a class of nonlinear discrete time delayed systems(NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov–Krasovskii functional method, a sufficient delaydependent condition for asymptotic stability of nonlinear systems is offered. Then, this condition is used to design a new efficient delayed state feedback controller(DSFC) for stabilization of such systems. These conditions are in the linear matrix inequality(LMI) framework. Illustrative examples confirm the improvement of the proposed approach over the similar cases. Furthermore, the obtained stability and stabilization conditions will be extended to uncertain discrete time delayed systems(UDTDS) with polytopic parameter uncertainties and also with norm-bounded parameter uncertainties.
基金supported by the National Natural Science Foundation of China(6133300561421063)the Research Fund for the Taishan Scholar Project of Shandong Province of China
文摘This paper deals with the problem of the optimal fault detection (FD) for linear discrete time-varying (LDTV) systems with delayed state and l(2)-norm bounded unknown input. The novelty lies in the designing of an evaluation function for the robust FD. The basic idea is to directly construct an evaluation function by using a weighted l(2)-norm of the measurement output, which achieves an optimal trade-off between the sensitivity to fault and the robustness to l(2)-norm bounded unknown input. To avoid complex computation, a feasible solution is obtained via the recursive computation by applying the orthogonal projection. It is shown that such an evaluation function provides a unified scheme for both the cases of unknown input being l(2)-norm bounded and jointly normal distribution, while a threshold may be chosen based on a priori knowledge of unknown input. A numerical example is given to demonstrate the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China(6117412161121003+2 种基金61203083)the Research Fund for the Doctoral Program of Higher Education of Chinathe Doctoral Foundation of University of Jinan(XBS1242)
文摘This paper deals with the problem of optimal fault detection filter （FDF） design for a class of discrete-time switched linear systems under arbitrary switching. By using an observer-based FDF as a residual generator, the design of the FDF is formulated into an optimization problem through maximizing the H_/H∞ or H∞/H∞ performance index. With the aid of an operator optimization method, it is shown that a mode-dependent unified optimal solution can be derived by solving a coupled Riccati equation. A numerical example is given to show the effectiveness of the proposed method.
基金Supported by National Basic Research and Development Program of China （973 Program） （2009CB320600）, National Natural Science Foundation of China （60774004）, Taishan Scholar Construction Engineering of Shandong Government, National Natural Science Foundation for Distinguished Young Scholars of China （60825304）
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 (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.
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.
文摘The robust H∞ filtering problem for uncertain discrete-time Markovian jump linear systems with mode- dependent time-delays is investigated. Attention is focused on designing a Markovian jump linear filter that ensures robust stochastic stability while achieving a prescribed H∞ performance level of the resulting filtering error system, for all admissible uncertainties. The key features of the approach include the introduction of a new type of stochastic Lyapunov functional and some free weighting matrix variables. Sufficient conditions for the solvability of this problem are obtained in terms of a set of linear matrix inequalities. Numerical examples are provided to demonstrate the reduced conservatism of the proposed approach.
基金supported by the National Natural Science Foundation of China(60710002)Self-Planned Task of State Key Laboratory of Robotics and System(SKLRS200801A03).
文摘This article deals with the robust stability analysis and passivity of uncertain discrete-time Takagi- Sugeno （T-S） fuzzy systems with time delays. The T-S fuzzy model with parametric uncertainties can approximate nonlinear uncertain systems at any precision. A sufficient condition on the existence of robust passive controller is established based on the Lyapunov stability theory. With the help of linear matrix inequality （LMI） method, robust passive controllers are designed so that the closed-loop system is robust stable and strictly passive. Furthermore, a convex optimization problem with LMI constraints is formulated to design robust passive controllers with the maximum dissipation rate. A numerical example illustrates the validity of the proposed method.
基金National Natural Science Foundation of P. R. China (50477042)Ph. D. Programs Foundation of Ministry of Education of P.R.China (20040422052)the Natural Science Foundation of Shandong Province (Z2004G04)
基金This project was Supported by the National Natural Science Foundation of China (50335020,60574011) PostdoctoralFund (2005038553) Science Research Important Foundation in Hubei Provincial Department of Education(2002z04001).
文摘A newly designed approach of simultaneous stabilization is given for linear discrete time-delay systems. The problem of stabilization for a collection of systems is discussed initially. Adequate condition are obtained in terms of linear matrix inequalities （LMIs） which are independent of time delays such that the resultant collection of discrete time-delay systems are stable with an upper bound of the quadratic performance index. Subsequently, controllers are designed such that the resultant closed-loop discrete time-delay systems are simultaneously stabilized with the upper bound of the quadratic performance index. Finally,a numerical example is given to illustrate the design method.
