Adaptive Guaranteed Cost Control for Time-delay Systems

In this paper, the guaranteed cost control with adjustable parameters for linear time-delay systems is studied. Firstly, the guaranteed cost controller with adjustable parameters is designed, and the sufficient condition for the controller existing is given in the form of LMI. And then, by designing the adaptive law of adjustable parameter, the adaptive guaranteed cost control is discussed. When adjustable parameters take different values, the guaranteed cost value and the feedback gains are also different. Different feed-back gains lead to different dynamic performance of closed-loop systems, therefore, the dynamic performance of closed-loop systems can be optimized and the guaranteed cost value can be reduced by choosing proper adjustable parameters. By designing adaptive law of the adjustable parameter, and introducing it into the stability conditions of closed-loop systems, the feedback gains which change with time are gotten. Compared with the results by fixed feedback gains, the proposed method leads to less conservatism. Simulation example is given to show the effectiveness of the proposed approach.