Study Of Guaranteed Cost Control For A Class Of Time Delay Uncertain Systems Based On T-S Fuzzy Model

Recently, the problem of designing robust controllers to make uncertain systems not only stable but also guarantee an adequate level of performance has drawn considerable attention. One approach to this problem is the guaranteed cost control approach first introduced by Chang and Peng. This approach is to design a controller such that the closed-loop system is asymptotically stable for all admissible uncertainties and the closed-loop cost function value is not more than a specified upper bound. It is well known that time-delays as well as parameter uncertainties are frequently the main cause of deterioration of systems performance and instability of systems. Therefore, the study of the guaranteed cost control for the uncertain time-delay systems has theoretic and practical significance, and has attracted considerable attention in the control theory literatures.In this dissertation, based on Lyapunov stability theory and linear matrix inequality approach, through using Tanakio and Sugeno model (T-S), we study the problems of guaranteed cost control for nonlinear time-delay systems with norm-bounded uncertainties. The main contents in this paper are as follows:1. Based on T-S fuzzy model, a fuzzy guaranteed cost control problem is studied for a class of uncertain discrete-time systems with multiple time delays. A Sufficient condition for the existence of fuzzy guaranteed cost control law and upper bound of cost function for the uncertain discrete-time systems with multiple time delays are given by choosing a proper Lyapunov function. And a design method for the fuzzy guaranteed cost control law is proposed in terms of liner matrix inequality method.2. Based on T-S fuzzy model, a fuzzy dynamic output feedback guaranteed cost control problem is studied for a class of uncertain discrete-time systems with multiple time delays, both for continuous-time and discrete-time case. A Sufficient condition for the existence of fuzzy output feedback guaranteed cost control law and upper bound of cost function for the systems are given by choosing a proper Lyapunov function. Furthermore, it is shown that this condition is equivalent to the feasibility problem of the linear matrix inequality. Based on that fact, the design method for the suboptimal fuzzy guaranteed cost control law is formulated as a convex optimization problem, which can be solved by recent convex optimization techniques.