Finite-time Stability And Robust Control Of Time-varying Descriptor Uncertain Systems

Time-varying descriptor systems are power systems which have more extensiveapplication than the normal time-invariant systems, it is described for many phenomenaand mathematical models in the chemical, physical, economic, ecological and biologicalprocesses. With the development of research, domestic and international many scholars puttheir attention to the time-varying descriptor system theory research, but the research isstill rare.In this thesis, based on time-varying descriptor systems, finite-time stability androbust finite-time stable control problems of time-varying descriptor systems is studied bythe theory of Lyapunov function, LMI, Schur technology and Riccati equation, mainsolution is that turns the finite-time stability problems into the LMI solving problems.We firstly discuss the asymptotic stability of time-varying descriptor systems.Sufficient conditions for the asymptotic stability of time-varying descriptor systems aregiven according to Lyapunov function theory, the Riccati equation, and asymptoticallystable state feedback controllers of time-varying descriptor systems and time-varyingdescriptor uncertain systems are designed. By a numerical example illustrates theeffectiveness of the conclusion.We secondly research the finite-time stability and control problems of time-varyingdescriptor systems. Research of system model is a class of time-varying descriptor systemswith disturbances. Sufficient conditions for the finite-time stability of time-varyingdescriptor systems and time-varying descriptor uncertain systems are given by Lyapunovtheory, the LMI and Schur lemma. Moreover, for finite-time stability and robust finite-timestability, the design methods of controller are given, the designed controller can guaranteesystem could normal operation when disturbance happens in a certain time interval. Anumerical example is used to demonstrate the conclusion.We finally study the input-output finite-time stability and control problems oftime-varying descriptor systems. Two kinds of models that time varying and time varyinguncertain descriptor systems are analyzed for interferencew2, w￥, the input-output finite-time stability control problem and robust input-output finite-time stability problemare discussed, respectively. Two kinds of the state feedback controllers’ design methodbased on LMI are also given, such that the system can reach input-output finite-timestability control.