Stability Analysis And Control Of Switched System With Time Delay

Hybrid dynamic systems are a class of systems which contain both discrete event dynamic systems and continuous or discrete time dynamic systems,and among them there exists interaction.Switched systems are an important class of special hybrid dynamic systems,which are composed of a family of subsystems and a rule orchestrating the switching between the subsystems.Switched systems are widely used in many practical problems,such as communication networks,electric systems,robotic walking control systems and sampled-data control systems,et al.Therefore,the investigation of switched systems is very necessary.Moreover,time-delay is an universal phenomenon existing in control systems which we can not ignore.It is the major reason to reduce system performance and even make system unstable.The analysis and control synthesis of linear switched systems with time-delay are discussed in this paper.The main contents of this paper are listed below:Firstly,stability analysis via feedback of linear systems with state delay that are composed of polytopic uncertain subsystems is studied.By combining with Leibniz-Newton formula and appropriate matrix inequality technique,some stability conditions of both delay-independent and delay-dependent are derived using Lyapunov-Razumikhin stability theory.Furthermore,we propose the switching rules by using the obtained common matrices.Then,the problem of H_∞control for a class of linear switched systems with timedelay is investigated.For switched system composed of a family of linear subsystems with time-delay,the synthesis of switching strategy is concerned with the optimization of H_∞performance.Both delay-independent and delay-dependent conditions for the problem of optimization of H_∞performance are derived.Furthermore,the switching state feedback strategies are proposed to solve the H-∞control problem for linear delay switched systems.