Robust H_∞ control of uncertain linear system with interval time-varying delays by using Wirtinger inequality

This paper is concerned with the robust H_∞ control problem of uncertain linear system with interval time-varying delays. Firstly, by using Wirtinger inequality approach, after constructing a new Lyapunov functional, the novel robust delay-dependent stability and stabilization criteria are developed. These improved results are expected to have less conservatism, due to the utilization of Wirtinger inequality and consideration of the information of the lower bound of time delay. Secondly, based on the obtained criteria, the memoryless H_∞ state feedback controller design scheme is presented, thus robust H_∞ controller design and performance analysis for uncertain linear system are developed. For a prescribed H_∞ performance level, the designed robust H_∞ controller can guarantee the uncertain linear system to be robustly stable and endure a larger delay. At last, numerical examples are provided to illustrate the effectiveness and superiority of the developed results.