Robust Controller Design for Time Delay Systems with Varying Parameters

In this paper, a comprehensive study is presented on the problem of designing a robust controller for time delay systems with varying parameters by using H-infinity static output feedback. The motivation for this work is the need for a control strategy that can handle both external disturbances, uncertainties and time-varying delays in linear parameter varying (LPV) systems which have wide applications in various fields. A novel synthesis method is proposed based on a quadratic Lyapunov-Krasovskii functional which is used to derive a sufficient matrix inequality condition via a Jensen-type integral inequality. We introduce an iterative algorithm to efficiently search for a feasible solution set for the synthesis problem. In addition to the proposed synthesis method, a comprehensive review of existing literature on robust control for LPV systems with time-varying delays is also provided. Various techniques are compared and contrasted and their advantages and limitations are highlighted. Therefore, the readers are equipped with a balanced view of the state-of-the-art in this field such that our proposed method is put into context. To demonstrate the effectiveness of the proposed approach, a numerical example is presented, along with comparison analysis. The results show that our method outperforms existing methods in terms of both stability and performance. Overall, this work offers a valuable contribution to the field of control engineering with potential applications in a variety of industries.