Study On Guaranteed Cost Control For Stochastic System With Time Delays

In present society, uncertainty and time-delay are ubiquitous phenomenon in controlsystem, their existences are the chief factors that lead to the instability and poorperformance of the system. Therefore, it becomes a hot issue in the control field to inhibitthe decline of performance caused by time-delay and reduce the conservative of system.Stochastic system is such a system that contains random variable such as parametersperturbations in internal structure, random disturbance of external environment andrandom errors of state measurement. To sum up, the study on guaranteed cost control fortime-delay uncertain stochastic systems has an important research significance in a way.This article discusses the following approaches of design guaranteed cost controller andguarantee robust stability for several time-delay uncertain stochastic systems.In Chapter Two, the problem of guaranteed cost control for a class of uncertainstochastic systems with multiple time-delays and nonlinear perturbation is presented. Theobject of this Chapter is to design a state feedback controller that can not only ensure theclosed-loop system is robust asymptotically stable, but also guarantee that the quadraticperformance index is less than a given upper bound. In the framework of Lyapunovfunction approach and linear matrix inequality (LMI) method, the sufficient condition forexistence of the controller is derived in the form of linear matrix inequality when theclosed-loop system is asymptotically stable. Finally, an example illustrate the effective ofthe design method.In Chapter Three, the robust H_∞guaranteed cost control for a class of nonlinearuncertain time-delay stochastic systems is addressed. The purpose of this Chapter is todesign a controller to ensure the closed-loop system is robustly H_∞asymptotically stable.The sufficient condition for robust H_∞asymptotic stability and the formation ofguaranteed cost controller are obtained by using Lyapunov stability theory and linearmatrix inequality method. At last, two numerical simulation are purposed to show thefeasibility of this method.In Chapter Four, a guaranteed cost control problem is developed for a class ofuncertain neutral stochastic systems with several time-delays. By using Lyapunov stabilitymethod, Ito formula, Schur complement lemma and linear matrix inequality, theguaranteed cost controller is designed and the controller can not only ensure theclosed-loop system is asymptotically stable, but also guarantee the given cost function has the determinate upper bound. Finally, a numerical simulation is used to demonstrate theeffectiveness of the approach.