Pulse Stability Of Switched Systems

In the first part of this thesis, by using Cauchy matrices of linear differentialsystems, the linear impulsive switched systems and the nonlinear impulsive switchedsystems with nonlinear disturbs are investigated. The systems are constituted offinite differential systems under some switching models and impulsive controls. Somesufficient conditions for exponential stability of the systems are established. The effectof impulse and of switching on the stability of the impulsive switched systems is alsodiscussed here.For a switched systems constituted of finite differential systems under someswitching models, there may be some switching models such that the stability ofeach differential system can't ensure the stability of the switched systems. In the sec-ond part of this thesis, a class of nonlinear impulsive switched systems effected by thefixed impulse is considered. The exponential stability of the systems is investigatedby using Lyapunov function and dwell time when all subsystems are exponentiallystable, or only a part of subsystems are exponentially stable. Some sufficient condi-tions for exponential stability of the systems are established. In addition, the designalgorithm of switching model is obtained. Simulation is given to show the efficiencyof the proposed results.In the Third part of this thesis, a class of two second order linear time-varyingimpulsive switched systems with delay is studied by using Lyapunov function. It isshowed that, for the exponential stability of the switched systems, some suitable con-trols are just only added on the subsequence of switching intervals for every subsystemthat can make the systems exponentially stable. The controls here are weaker thanthe conditions which make every subsystem exponentially stable. The design methodsof switching model and of impulsive controls is also given.In the last part of this thesis, the uniform stability and the uniform asymptoticalstability of a class of nonlinear impulsive switched systems with delay is investigatedby using Lyapunov-Razumikhin functional.Some sufficient conditions for the stabilityof the systems are established.