Control Design Of Two Kinds Of Switching Time - Delay Systems

Singular systems with Markov jump parameters and complex interconnected systems are an important switched system and widely applied in digital communication networks, power system, industrial process control and so on. They attracts the attention of the domestic and foreign scholars, becoming one of the hottest topic of theoretical research. On the other hand, time delays are often encountered in various systems which cause the instability of systems. However, the results obtained in the existing references on dissipativity for singular systems with Markov jump parameters are more conservative. Moreover, study on sliding mode control of the complex interconnected systems are based on the ideal conditions, such as the system states are observable fully and the interconnections are known exactly. In fact, the condition are not be satisfied usually because of the uncertainty of the system and non-fragility of controller. In this paper, the above problems is studied for two classes of switched systems. It includes two parts as follows:1. Dissipativity control of singular systems with Markov jump parameters and mode-dependent mixed time delaysThe robust dissipativity problem for singular systems with Markov jump parameters and mode-dependent mixed time delays are studied. The system uncertainty, mode-dependent mixed time delays, Markov jump parameters and singular phenomenon exist in the systems simultaneously. So far, many results on the dissipativity problem of singular systems with time delay have been established. But for singular systems with Markov jump parameters and mixed time delays, there are few studies on its dissipative problem. Through introducing a new mode-dependent Lyapunov- Krasovskii functional, some sufficient conditions are derived to ensure the stability of the system and the robust dissipativity. Compared with the existing literature, the obtained results are less conservative.2. Adaptive output feedback sliding mode control for complex interconnected time-delay switched systemsFor a class of complex interconnected switched systems with time delay, the sliding mode control problem is studied. The unobserved system states, mismatched parameter uncertainties in the state matrix of each isolated subsystem, mismatched uncertain interconnections and unknown exogenous disturbance exist in the systems simultaneously. Firstly, for each subsystem, a sliding mode surface depending on only the output is designed by reduction of order. Then, based on the designed sliding mode surface, a Lyapunov-Krasovskii functional is given to analyze the stability of systems, and the sufficient conditions are obtained to guarantee the asymptotic stability on the sliding mode surface. Finally, based on a new theorem,an adaptive output feedback sliding mode control law is constructed which removes some constraints in the existing literature.