Dissipative Control For Continuous Stochastic Systems

Since the notation of dissipative dynamical system was introduced by Willems in 1972,it has played a very important role in systems,circuits,network and control engineering and theory. Dissipativeness is a generalization of the concept of passiv-ity in electrical networks and other dynamical systems which dissipate energy in some abstract sense. Recently, the theory of dissipative systems generalizes basic tools in-cluding the passivity, bounded real lemma, Kalman-Yakubovich lemma and the circle criterion. As the notion of dissipativeness provides a flexible tradeoff between gain and phase,it can be an appropriate framework for a less conservative robust controller design, especially in applications where both gain and phase are considered.Stochastic systems have recently received considerable attention since stochastic modeling has come to play an important role in many branches of science and engineer-ing applications.In many practical systems such as aircraft systems or biology systems or electronic circuits,there always exist some unavoidable stochastic perturbations that should be taken into consideration in system design and performance analysis.Thus,it is of great importance both in theoretical and practical application to study dissipative control of stochastic systems and stochastic singular systems.In this thesis,our attention is focused on the design of state-feedback dissipative controller for stochastic systems and stochastic singular systems such that the closed loop systems is mean-square asymptotically stable and strictly (Q, S,R)-dissipative. The main work of this dissertation are outlined as follows:(1)The stochastic stability and strict dissipativeness analysis for wireless channels systems modeled by stochastic differential equation are presented. Consider Eu-ler's method,stochastic trapezoidal method and Lyapunov functions method to study the asymptotical and mean square stability for wireless channels model, respectively. Propose a sufficient condition in term of linear matrix inequality (LMI) to guarantee the stochastic stability in the mean square and strict (Q,S,R)-dissipativeness.(2) We deals with the problem of dissipative control for stochastic systems with state delay. The state delay is assumed to be time-varying.Attention is focused on the design of linear memoryless state feedback controller based on Lyapunov-Krasovskii functional approach such that the closed-loop systems is exponentially stable in the mean square and strictly(Q,S, R)-dissipative.The expressions of desired state feedback controller is given. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed approach. Our result unifies the existing results on H∞and passive control for stochastic systems with state delay and provides a more flexible and less conservative control design as it allows for a better trade-off between phase and gain performance.(3)Based on the extended Ito stochastic differential formula, the problem of dissi-pative control for stochastic singular systems and a class of stochastic singular time-delay systems with nonlinear perturbations are studied. Attention is focused on the design of linear memoryless state feedback controller based on Lyapunov-Krasovskii functional approach such that the closed-loop systems is mean-square asymptotically stable and strictly(Q,S,R)-dissipative.Sufficient conditions for the solvability of these problem are obtained in terms of LMIs.Finally, il-lustrative examples are provided to demonstrate the effectiveness of the proposed approach.