Output Feedback Control Synthesis for Linear Time-Delay Systems via Infinite-dimensional LMI Approach

This paper considers synthesis problems of output feedback controllers for linear time-delay systems via infinite-dimensional Linear Matrix Inequality (LMI) approach. Based on our recent work considering synthesis problems of stabilizing dynamic output feedback controllers which guarantee the internal stability of the closed loop systems, we derive existence conditions and explicit formulas of two different dynamic output feedback H _∞ controllers, which guarantee the internal stability of the closed loop systems and a prescribed level of L ₂ gain of closed loop systems. The derived dynamic output feedback H _∞ controllers can be interpreted as controllers which consist of memory state feedback controllers and memoryless/memory observers which have new observer structures. Next, we introduce a technique to reduce conditions for synthesis in the form of infinite-dimensional LMIs to the finite number of LMIs, and present a feasible algorithm for synthesis of output feedback H _∞ controllers based on the finite-dimensional LMIs. Finally we demonstrate the efficacy of the proposed output feedback H _∞ controllers by numerical examples.