Robust Non-fragile Control And H_? Filter Designing For Switched Singular Systems

The problems of non-fragile robust control and robust H? filtering are studied for uncertain switched singular systems with time-varying delay in state.The common Lyapunov function method,multiple Lyapunov functions method and average dwell time method are used in this paper.In addition,the convex combination technique and Linear Matrix Inequalities(LMIs)technique are also applied in this paper.The main contents are summarized as follows:(1)The problem of delay-dependent non-fragile robust H? control is studied for a class of uncertain switched singular systems with time-varying delay in state.Delay-dependent sufficient conditions are presented,which make the closed-loop system constituted by the original system and designed controllers asymptotically stable with the robust H? performance index y under the designed switching rule,by using multiple Lyapunov functions method and integral inequalities.Secondly,the LMIs technique is used to linearize the sufficient conditions mentioned above,and designs for parameters of non-fragile state feedback controllers with additive perturbations and the corresponding switching rule are given.Furthermore,algorithms of finding the minimum robust H? performance index ?min and the upper bound of delay are given.Finally.an example is given to demonstrate the validity of the above conditions and algorithms.(2)The problems of exponential stability and weighted L2 gain for the above system are studied by using the average dwell time method and the steps in(I).(3)The problem of robust H? filtering is studied for a class of nonlinear,uncertain switched singular systems with time-varying delay in state.The asymptotic stability with robust H? performance of the filter error system constituted by the original system and designed filters is analyzed by using the common Lyapunov function method and the convex combination technique.Secondly,the sufficient conditions in the form of LMIs.which make sure the existence of filter,are listed,and designs for parameters of the filter are given.Finally,a numerical example is given to show the rationality of the designs.(4)The problem mentioned above is studied further under the above steps,by using the multiple Lyapunov functions method,when the filter error system has non-vanishing delay lower bound.What's more,it's extended to the situation where the infimum of the delay is zero.Delay-dependent sufficient conditions are obtained,and designs for parameters of the filter with the minimal robust H? performance index are given.