Robust H_∞ Control And Guaranteed Cost H_∞ Control Of Uncertain Time-Delays Systems

In many engineering systems,the uncertainty is always inevitable. The uncertainty can reflect the substantial control process accurately, and manifest the exterior disturbance and the parameter variation of the system. On the other hand,owing to the complexity and multiplicity of the system, it always has the time-delay. Comparing with the non-time-delay system, the time-delay existence not only increases the difficulty in the analysis and the practice application, but also leads control system performance to be worse, hardly to guarantee the stability of closed-loop system. Because of the widespread existence and the difficulty in the analysis and synthesis of the time-delay, there are important theoretic and practical significance in the robust stability and control of the uncertain time-delay system.The robust H∞control and the guaranteed cost H∞control of the uncertain time-delays systems are studied, based on the Lyapunov stability, H∞control theory and linear matrix inequality method. The primary tasks are as follows:1.The guaranteed cost control and index stability of uncertain discrete-time system with time-delay are discussed. According to Lyapunov function and linear matrix inequality method, the sufficient conditions for the existence of guaranteed cost controller and the time-delay dependent index stability are given.2.In view of uncertain discrete-time system with time-delay, the robust H∞control is studied. Using the quadratic stability theory and linear matrix inequality methods, the sufficient condition of robust H∞control and H∞memory state feedback controller are gotten.3.The time-delay dependent robust H∞control of the uncertain discrete-time systems with time-delay is discussed. Via the Lyapunov functional method, the time-delay dependent H∞state feedback controller is designed. 4.A class of complex continuous uncertain system with multiple delay time is researched. When the perturbation of controller is additive and multiplicative, the non-fragile guaranteed cost H∞controller is designed via Lyapunov function and linear matrix inequality.Finally, the non-fragile guaranteed cost H∞controller with multiple time-varying delay is designed,and a sufficient condition is proved and given for the solvability of the non-fragile guaranteed cost H∞control problem.