Two Categories Of Switched Systems With Delay Robust Control Problem,

In recent years, there has been growing interest in stability analysis and controller design for hybrid and switched systems. By a switched system, we mean a hybrid dynamical system consisting of a family of continuous-time or discrete-time subsystems and a rule that orches-trates the switching among them. The motivation for studying hybrid and switched systems mainly comes from the fact that they provide a natural and convenient unified framework for mathematical modeling of many physical phenomena and practical applications. Typical examples include autonomous transmission systems, computer disc driver, room temperature control, power electronics, chaos generators. Therefore, we pay more important attention on Delay-dependent l2-l∞control for uncertain discrete-time switched systems with mode-dependent time-varying delays and Robust H∞stabilization for uncertain switched impulsive control systems with state delay.1) Delay-dependent l2—l∞control for uncertain discrete-time switched systems with mode-dependent time-varying delays:The parameter uncertainties are assumed to be time-varying but norm-bounded. The purpose is to construct a switched state feedback controller such that the resulting closed-loop system is asymptotically stable while satisfying a prescribed l2—l∞performance level irrespective of the parameter uncertainties and time-varying delays. By resorting to a re-cently developed finite sum inequality approach and using the linear matrix inequality(LMI) technique, delay-dependent conditions for the solvability of the problem are developed.2)Robust H∞stabilization for uncertain switched impulsive control systems with state delay:we mainly deal with the problem of robust H∞state feedback stabilization for uncertain switched linear systems with state delay. The system under consideration involves time delay in the state, parameter uncertainties and nonlinear uncertainties. The parameter uncertainties are norm-bounded time-varying uncertainties which enter all the state matrices. In addition, the impulsive behavior is introduced into the given switched system, which results a novel class of hybrid and switched systems called switched impulsive control systems. Using the switched Lyapunov function approach, some sufficient conditions are developed to ensure the globally robust asymptotic stability and robust H∞disturbance attenuation performance in terms of certain linear matrix inequalities(LMIs). Finally, the effectiveness of the algorithms is illustrated with an example.