Study On Guaranteed Cost Control For Nonlinear Systems With Time Delays

There are inevitable time delays in a large number of natural and social phenomena. Namely, the development trend of things not only depends on the current state, but also relies on the past of things. The control of time delay systems is an important field of control theory. Time delay cause deterioration of system, and even unstable, will greatly damage performance of control system. The existence of time-delay system can often reduce performance index, and even can cause stability of the system. How to suppress the delay caused the system performance and to reduce the system conservative became a hot and difficult problem in control field. Therefore, the study on the guaranteed cost control for time delay systems have a important theoretical and practical value. This paper studies stability and guaranteed cost controller or filter design for several uncertain nonlinear systems with time delay. The organization of this dissertation is as follows:In chapter two, the problem of the guaranteed cost control for a delay-dependent nonlinear singular system is studied. The purpose is to design a memory state feedback controller, the closed-loop system is asymptotically stable and the corresponding performance index is not more than a certain bound. Based on Lyapunov function method and the linear matrix inequality (LMI) technique, a sufficient stabilization condition of closed-loop system and explicit expressions of guaranteed cost control are obtained. Finally, the effectiveness of the proposed method is proved by a numerical example.In chapter three, the problem of H2 guaranteed cost control for singular stochastic neural networks with distributed delays is saved. The aim of this paper is to prove neural networks are stochastically asymptotically stable in the means quare for all admissible parameter uncertainties and the cost function value is not more than a specified upper bound. Based on Lyapunov stability theory and LMI techniques, a sufficient stabilization condition is derived. Finally. a numerical example has shown the feasibility and effectiveness of the mentioned results.In chapter four, the non-fragile H∞guaranteed cost control problem of uncertain non-linear stochastic neutral systems is considered. A sufficient stabilization condition is proposed based on Lyapunov stability theory combined with LMI technique. Furthermore. a sufficient condition for the existence of the controller is presented and the cost function value is not more than a specified upper bound by LMI. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed techniques. Last but not the least, the robust H∞guaranteed cost filter problem of a class of uncertain nonlinear time-delay stochastic systems is considered. A robust H∞guaranteed cost filter is designed such that for all uncertainties, the resulting augmented system is robustly asymptotically stable and satisfies the proposed guaranteed cost performance. In terms of Lyapunov stability theory and LMI technique. a sufficient stabilization condition is derived and robust H∞guaranteed cost filter is designed. Finally, a numerical example is shown to demonstrate the usefulness of the proposed techniques.