Stability Analysis And Synthesis Of Several Singular Systems With Markovian Jump Time-varying Delay

In the past few decades,due to the extensive applications of the singular systems in chemical process,power system,nuclear reactor,robotic manipulator systems,biological systems,the singular systems have received considerable attention.Meanwhile,the stability of the general systems is more important in the study.In order to describe the natural phenomena more accurately,we consider the influence of the time-varying delay on system stability.This paper is divided into three parts:In the first part of this dissertation,observer-based integral sliding mode control of phase-type semi-Markovian jumping singular systems is considered.Observer-based surface define Lyapunov function and a sliding mode controller is synthesized to ensure that the associated Markovian jump singular system satisfies the reaching condition.Meanwhile,Lyapunov stability theory is used to obtain the sufficient conditions of stability.A simulation is given to illustrate the effectiveness of the theoretical results.In the second part of this dissertation,the mean square admissibility problem of a class of Markovian jump singular systems subject to deterministic switching and stochastic jumps with generally uncertain transition rates is considered.Based on liner matrix inequality,some sufficient conditions of the mean square stability and admissibility of the switching Markovian jump singular systems with generally uncertain transition rates are given.Then,the problem of the mean square admissibility of the switching Markovian jump singular systems with partly unknown transition rates is discussed.Finally,a numerical example is given to illustrate the effectiveness of the theoretical results.In the third part of this dissertation,H? performance for delayed singular nonlinear Markovian jump systems with unknown transition rates is considered.Based on ?Ito differential formula and Lyapunov stability theory,we proposed a new class of robust controller,which is composed of a linear controller and an adaptive controller,to guarantee the given system is stochastically admissible.Finally,a numerical example is given to illustrate the effectiveness of the theoretical results.