Stabilization Of Linear Switched Systems With Large Time-varying Delay Periods Under Asynchronous Switching

Switched systems as a special class of hybrid dynamical systems have profound theoretical research significance and extensive actual application background,The.switched systems are composed of a set of discrete or continuous subsystems and a switching signal,which coordinates the switching sequence and switching time of these subsysterms.Stability as a major feature of the systems has been widely used in the analysis and design of switched systems,beca.use the switched systems consist of several subsyst.ems and the switching mode of these subsystems can affect the stability of the systems,so they are differ from the general systems,as we all know,time delay phenomenon is inevita.ble in t.he practical engineering control,small delay ha.s little effect on system stability,but if the delay exceeds a certain upper bound,it will lead to system instability or ba.d performance,therefore t,he study for the stability analysis and stabilization of a class of switched systems with large time-varying delay problem is very necessary.The paper focuses on state feedback stabilization problem for a class of linear switched delay systems with large time-varying delay periods under asynchronous switching.Main goal is to design state feedback controllers to make the closed-loop system stable.The switching signal of controllers is supposed to be with delay,which leads to the asynchronous switching between the system modes and controller modes.The original systems under consideration are assumed to be stable during small delay periods(SDPs)and be unstable during large delay periods(LDPs).Under the constraint of the length rate of unstable periods and the frequency of LDPs,by constructing a novel piecewise Lyapunov functional,some sufficient conditions for exponential stability are derived.The controller design problem is solved by utilizing the cone complementarity lineaization,which can be turned into a minimization problem subject to LMI constraints.Finally,a example is given to illuminate the effectiveness of the given results.