The Stability Analysis And Robust Control For Singular Markovian Jump System

Markov jump system is a kind of special hybrid system, which can better describe the random mutation of the physical system, and it has been widely used in communication system and control system, such as satellite system and chemical industry process control. At present, the research of the singular Markov jump system has attracted the attention of the majority of scholars, it has important theoretical value and practical significance to study the stability and robust control of the system.This paper studies the exponential stability, H?control and passive control for singular Markov jump systems with time delay by constructing appropriate LyapunovKrasovskii function, combining with free-weighting matrix, weak infinitesimal operator, integral inequality and other methods.The main contents are as follows:First of all, the exponential stability of the singular Markovian jump system with time-varying delay was analyzed and discussed. By using the Lyapunov function theory, the design of the output feedback controller is obtained such that the closed-loop system is mean-square exponentially admissible.Secondly, the H?control problem of singular Markovian jump systems with timevarying delay is discussed. By constructing appropriate Lyapunov function and free-weighting matrix method, a sufficient condition which ensures the considered system is stochastically admissible with given H?performance index is derived, and the controller design method is given. Finally, some numerical examples are provided to show the effectiveness of the proposed approach.Thirdly, for a class of uncertain singular Markov jump systems with time-varying delay and norm-bounded parameter uncertainties, the observer-based passive control problem is studied via a novel Lyapunov function including mode-dependent double integral terms, and a criterion is given to ensure the system is regular, impulse free and stochastically stable. Then, the observer-based passive controller is designed.Finally, the problem of observer-based H?control for nonlinear singular Markov jump system with time delay is studied. The exponential stability criterion of the system is obtained by using the integral inequality method and the weak infinitesimal operator, then, the observer-based H?controller is designed.