Robust Dissipative Control For Singular Markovian Jump System

Markovian jump system is a kind of special hybrid system, which can describe the random mutation phenomenon of the physical system, and it has a wide range of appli-cations in the control engineering, such as satellite system and chemical industry process control. At present, the research of the singular Markovian jump system attracts the attention of the mojority of scholars, it has important practical significance to study the control problem of the system. In this paper, we study the exponential stability, H?control and dissipative control for the singular Markovian jump system with time-varying delay. The main contents are as follows:1. The problem of stability and dissipative control for singular Markovian jump sys-tem with time-varying delay and uncertainty is studied. By constructing appropriate Lyapunov function, the sufficient condition for stability and dissipation of system is ob-tained by linear matrix inequality method, then state feedback controller is designed to make the closed-loop system be stable and dissipative.2. The problem of exponential dissipativity and exponential passive for the singular Markovian jump system with time-varying delay and uncertainty is discussed. With the Lyapunov function and the Newton-Leibniz formula, the sufficient conditions for expo-nential dissipativity and exponential passive of the system are obtained.3. The problem of exponential mean square stability and H? control for singular Markovian jump system with time-varying delay and uncertainty is studied. A state feed-back controller on Lyapunov function and stochastic differential equations is designed to make the closed-loop system exponential mean square stability and satisfy H? perfor-mance for all admitted uncertainties, and there exists a minimum upper bound. Then the feasibility of the conclusions is verified by sone numerical examples.