Robust Stability Analysis And Control Of Some Classes Of Nonlinear Stochastic Systems

With the development in technics, the demand for the accuracy of control systems inpractical applications becomes much more critical, but deterministic system model can-not meet the high requirement of precision. In addition, stochastic factors and time-delayare often the source of performance degradation and instability. Therefore, the study ofstability and controller design for nonlinear stochastic time-delay systems has become aserious problem. It is well known that the adaptive estimation method is very effectiveto approximate unknown parameter in systems. But the study of parameter estimationand adaptive control for nonlinear stochastic systems with unknown parameter is diffi-cult because of the influences of stochastic factors. This dissertation studies the stabilityand controller design for nonlinear stochastic systems by using stochastic Lyapunov sta-bility theory, the properties of the stochastic integral, the linear matrix inequality(LMI)technique and the separation theory of parameter. Studies and main results include thefollowing several respects:Applying a Lyapunov-Krasovskii functional combined with the linear matrix in-equality technique, New delay-dependent stability criteria are give based on an one-sidedLipschitz condition and a quadratic inner-boundedness condition. The less conservativestability conditions of uncertain stochastic nonlinear time-delay systems are developedin term of LMI. A non-fragile state feedback controller which can guarantee the robuststochastic stability of the closed loop systems is designed, and non-fragile robust H∞controller is given to make closed systems meets specific H∞ performance.The observers design problem of a class of Lipschitz stochastic discrete-time sys-tems is studied. Since there can be make better use of the structural knowledge of thenonlinear part, a generalized Lipschitz condition is first introduced to the observer designfor a class of nonlinear stochastic discrete-time systems. Both the full-order and reduced-order observer design for nonlinear discrete-time systems without stochastic factor areinvestigated. And then the research methods for deterministic discrete-time systems areextended to stochastic systems. A new observer synthesis conditions are derived by usinga LMI-based techniques and theory of the quadratic stability.Adaptive observer design problem for both the nonlinear stochastic continuous sys-tems and discrete system is considered. Unknown constant parameters are assumed to benorm bounded in system. In order to better use the structural knowledge of the nonlinearpart, a generalized Lipschitz condition is introduced to the adaptive observer design ofnonlinear stochastic systems. Based on a Lyapunov-Krasovskii functional approach andstochastic Lyapunov stability theory, new adaptive observer design condition with ulti-mately exponentially bounded in sense of mean square for errors systems is presented interms of linear matrix inequality.The state estimation and state-feedback stabilization problems for a class of non-linear stochastic systems with unknown constant parameters are studied. New designmethods are proposed to construct the adaptive controllers. Adaptive state and parameterestimators are designed by using stochastic Lyapunov method and the separation theoryof the design for the state-feedback gain and observer gain, which guarantees that theclosed-loop system is stochastic stable. And then the research methods are extended tostochastic time-delay systems. Sufficient conditions for the existence of parameters esti-mator are obtained. Finally, the summary of this dissertation and prospect of the researchdevelopment are given.