Memory observer-based output feedback control for linear time-delay systems

This paper considers synthesis problems of stabilizing dynamic output feedback controllers for linear time-delay systems via infinite-dimensional Linear Matrix Inequality (LMI) approach. We derive an existence condition and an explicit formula of dynamic output feedback controllers for linear time-delay systems, which guarantee the internal stability of the closed loop systems. The derived dynamic output feedback controllers can be interpreted as controllers which consist of memory state feedback controllers and memory observers. Next, we introduce a technique to reduce conditions for synthesis in the form of infinitedimensional LMIs to a finite number of LMIs. and present a feasible algorithm for synthesis of controllers based on the finite-dimensional LMIs. Finally we demonstrate the efficacy of the proposed dynamic output feedback controllers by a numerical case study.