Robust H_∞ Control And Stability Of Descriptor Switched Systems

Descriptor systems,are also called singular systems,have more extensive sense than normal systems.Switched systems composed of several subsystems and a switching law that specifies the active subsystem at each instant of time.If all of the subsystems are singular systems,we called them descriptor switched systems.Time-delay is a widespread natural phenomenon;the change rate in current state of time-delay systems not only depends on the current state,but also depends on the past state.Time-delay descriptor switched systems,the descriptor switched systems with time-delay,are more general systems.On the basis of the recent progress of theory and methods on descriptor systems and switched systems,this dissertation implements a systematic study on the stability,and H_∞control for descriptor switched systems and uncertain descriptor switched systems with time-delay,by means of LMI techniques.The main results obtained in this dissertation are summarized as follows:First,the stability of the descriptor switched systems is researched.In order to avoid the problems brought about by solving the matrix inequality with equation restriction,the results are not given based on an equation or a matrix inequality form.For a class descriptor switched systems with uncertain interval matrix,the robust stability is studied with the research methods in stability of descriptor systems and switched systems.Two switching strategies are designed by the completeness condition and the methods of multi-Lyapunov,respectively.The sufficient conditions for stability of the systems are also given.Then,the features of H_∞control for descriptor switched systems are considered.By multi-Lyapunov method,the design of state-feedback controller for a class of uncertain descriptor switched systems is obtained,and the sufficient condition which can stabilize the systems and satisfy H_∞performanceγis also given.Finally,by using the integral inequality,the H_∞control and stability of the descriptor switched system with time-delay are studied.On the basis of learning the methods of controller design for the common systems,the design of state-feedback controller for a class of uncertain descriptor switched systems with time-delay is obtained,and the delay-dependent stable sufficient condition which can stabilizes the systems and satisfies H_∞performanceγis also given.Numerically calculating examples are given to validate the correctness and effectiveness of the results in every part of the dissertation.