Robust H_∞ Control For Large-scale Uncertain Discrete Systems With Time-delay

Uncertainty and time-delay are existed in real industrial process systems. The introduction of uncertainty and delay into the system describes the difference between the mathematic model and controlled plant, which reflects the existance of the variation of the system parameters and disturbance. In a ward, it is of a great importance in theoretical and practical. The robust control theory is an effective way to deal with the uncertainty parameters, however, it's not enough to just satisfy the robust stability. Linear quadratic performance (guaranteed cost performance) criterion can reflect a lot of performance requirements, therefore, how to design a guaranteed cost controller under which the closed-loop system is asymptotically stable for all admissible uncertainty and the closed-loop cost function value is not more than a specified upper bound has drawn considerable attention.Based on Lyapunov theory and H2 H∞control theory, linear matrix inequality method is adopted in this paper to study the robust and guaranteed cost H∞control problem for uncertain system. The main contents are as follows:Firstly, the problem of robust stability for the uncertain linear discrete-time systems with time-delay and nonlinear uncertain discrete-time systems with time-delay are studied and the problem of observer-based output feedback stabilization for uncertain discrete-time systems with time-delay is discussed. By using linear matrix inequality method the relevant conditions that the systems is robust stability are obtained and state feedback controllers are designed.Secondly, the problem of guaranteed cost H∞control during the quadratic stable period of uncertain discrete-time systems with time-delay is addressed. By using linear matrix inequality method the conditions of robust stability are presented and guaranteed cost H∞state feedback controllers are designed.Thirdly, the problem of observer-based guaranteed cost H∞control for uncertain discrete-time systems with time-delay systems is studied. The sufficient conditions of robust stability are obtained and the guaranteed cost H∞state feedback controllers and the observer are designed, by using linear matrix inequality methodFinally, the problem of decentralized guaranteed cost H∞control of large scale interconnected uncertain discrete time-delay systems is discussed. The conditions of robust stability are presented using linear matrix inequality method and guaranteed cost H∞state feedback controllers are designed, by using linear matrix inequality method...