Robust Control And State Estimation Of Stochastic Systems

This thesis investigates robust control and estimation of several different systems such as interconnected systems, singular systems, impulsive systems, networked control systems, in stochastic setting via a linear matrix inequality approach.Firstly, the robust decentralized control problem for interconnected systems with Markovian switching is studied. For an interconnected discrete-time system with finite Markovian jump, we present a design of a guaranteed cost decentralized state feedback control law. Based on Lyapunov method, the proposed decentralized control guarantees the robust stochastic stability of the resulting closed-loop system with a guaranteed cost performance index. Furthermore, the problem of the decentralized observer-based output feedback control is dealt with for uncertain interconnected Markovian jumping systems with sector nonlinearities.Secondly, the problem studied involves the observer design for a class of descriptor Markovian jumping systems with nonlinear perturbations. The design of full-order and reduced-order state observers are presented, respectively. The dynamics of each estimation error is guaranteed to be globally exponentially stable in the mean square. It is shown that the design of both types of state observers can be reformulated as the unified linear matrix inequality structure.Thirdly, for two classes of impulsive stochastic systems with uncertainties we are concerned with the robust H_∞ control and the disturbance rejection control problem, respectively. Based on linear matrix inequality approaches, the robust H_∞ control law and the disturbance rejection control law are designed, respectively. These controllers guarantee the robust stochastic stability of the corresponding closed-loop systems with their own prescribed performance level. The effectiveness of the proposed design approach are illustrated by numerical examples.Finally, the stochastic stability analysis and design of networked control sys-...