In this paper, we directly use the tirear norm Liapunov function to investigate the stability of the linear discrete large-scale systems and obtain some criteria for the asymptotic stability of such a system.
On the stability analysis of large-scale systems by Lyapunov functions, it is necessary to determine the stability of vector comparison equations. For discrete systems, only the stability of linear autonomous comparis...On the stability analysis of large-scale systems by Lyapunov functions, it is necessary to determine the stability of vector comparison equations. For discrete systems, only the stability of linear autonomous comparison equations was studied in the past. In this paper, various criteria of stability for discrete nonlinear autonomous comparison equations are completely established. Among them, a criterion for asymptotic stability is not only sufficient, but also necessary, from which a criterion on the function class C, is derived. Both of them can be used to determine the unexponential stability, even in the large, for discrete nonlinear (autonomous or nonautonomous) systems. All the criteria are of simple algebraic forms and can be readily used.展开更多
The decentralized robust guaranteed cost control problem is studied for a class of interconnected singular large-scale systems with time-delay and norm-bounded time-invariant parameter uncertainty under a given quadra...The decentralized robust guaranteed cost control problem is studied for a class of interconnected singular large-scale systems with time-delay and norm-bounded time-invariant parameter uncertainty under a given quadratic cost performance function. The problem that is addressed in this study is to design a decentralized robust guaranteed cost state feedback controller such that the closed-loop system is not only regular, impulse-free and stable, but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of the decentralized robust guaranteed cost state feedback controllers is proposed in terms of a linear matrix inequality （LMI） via LMI approach. When this condition is feasible, the desired state feedback decentralized robust guaranteed cost controller gain matrices can be obtained. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed approach.展开更多
Based on Lyapunov stability theory, a less conservative sufficient condilions for the stabih＇lies of uncertain discrete delayindependent and delay-dependent control systems are obtained by using the linear matrix ine...Based on Lyapunov stability theory, a less conservative sufficient condilions for the stabih＇lies of uncertain discrete delayindependent and delay-dependent control systems are obtained by using the linear matrix inequality （LMI） approach. Judgement of the stability of time-delay systems is transformed to judgement of the feasible solution of an LMI, and hence is solved by use of MATLAB. Numerical simulations verify 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
In this paper, we study the output regulation problem of discrete linear time-delay systems by output feedback control. We have established some results parallel to those for the output regulation problem of continuou...In this paper, we study the output regulation problem of discrete linear time-delay systems by output feedback control. We have established some results parallel to those for the output regulation problem of continuous linear time-delay systems.展开更多
In this paper, the stability of nonlinear time-delay discrete systems is investigated bymeans of the Gauss-Seidel iteration method. Some algebraic criteria of the stability are obtained. Theconstruction of Lyapunov fu...In this paper, the stability of nonlinear time-delay discrete systems is investigated bymeans of the Gauss-Seidel iteration method. Some algebraic criteria of the stability are obtained. Theconstruction of Lyapunov function is avoided.展开更多
This paper focuses on the robust stability for time-delay systems of neutral type. A new complete Lyapunov-Krasovskii function (LKF) is developed. Based on this function and discretization, stability conditions in ter...This paper focuses on the robust stability for time-delay systems of neutral type. A new complete Lyapunov-Krasovskii function (LKF) is developed. Based on this function and discretization, stability conditions in terms of linear matrix inequalities are obtained. A class of time-varying uncertainty of system matrices can be studied by the method.展开更多
文摘In this paper, we directly use the tirear norm Liapunov function to investigate the stability of the linear discrete large-scale systems and obtain some criteria for the asymptotic stability of such a system.
文摘On the stability analysis of large-scale systems by Lyapunov functions, it is necessary to determine the stability of vector comparison equations. For discrete systems, only the stability of linear autonomous comparison equations was studied in the past. In this paper, various criteria of stability for discrete nonlinear autonomous comparison equations are completely established. Among them, a criterion for asymptotic stability is not only sufficient, but also necessary, from which a criterion on the function class C, is derived. Both of them can be used to determine the unexponential stability, even in the large, for discrete nonlinear (autonomous or nonautonomous) systems. All the criteria are of simple algebraic forms and can be readily used.
基金This project was supported by the National Natural Science Foundation of China (60474078)Science Foundation of High Education of Jiangsu of China (04KJD120016).
文摘The decentralized robust guaranteed cost control problem is studied for a class of interconnected singular large-scale systems with time-delay and norm-bounded time-invariant parameter uncertainty under a given quadratic cost performance function. The problem that is addressed in this study is to design a decentralized robust guaranteed cost state feedback controller such that the closed-loop system is not only regular, impulse-free and stable, but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of the decentralized robust guaranteed cost state feedback controllers is proposed in terms of a linear matrix inequality （LMI） via LMI approach. When this condition is feasible, the desired state feedback decentralized robust guaranteed cost controller gain matrices can be obtained. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed approach.
文摘Based on Lyapunov stability theory, a less conservative sufficient condilions for the stabih＇lies of uncertain discrete delayindependent and delay-dependent control systems are obtained by using the linear matrix inequality （LMI） approach. Judgement of the stability of time-delay systems is transformed to judgement of the feasible solution of an LMI, and hence is solved by use of MATLAB. Numerical simulations verify the validity of the proposed method.
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.
基金This work was supported in part by the Research Grants Council of the Hong Kong Special Administration Region （No. 412813） and in part by the National Natural Science Foundation of China （No. 611 74049）.
文摘In this paper, we study the output regulation problem of discrete linear time-delay systems by output feedback control. We have established some results parallel to those for the output regulation problem of continuous linear time-delay systems.
文摘In this paper, the stability of nonlinear time-delay discrete systems is investigated bymeans of the Gauss-Seidel iteration method. Some algebraic criteria of the stability are obtained. Theconstruction of Lyapunov function is avoided.
基金the National High Technology Research and Development Program (863) of China(No. 2006AA05Z148)
文摘This paper focuses on the robust stability for time-delay systems of neutral type. A new complete Lyapunov-Krasovskii function (LKF) is developed. Based on this function and discretization, stability conditions in terms of linear matrix inequalities are obtained. A class of time-varying uncertainty of system matrices can be studied by the method.
