Dynamical output feedback controller design for linear time-delay systems

This paper is concerned with the stabilization problem for linear time-delay systems. Attention is focused on the design of dynamical output feedback controller to stabilize the resulting closed-loop system. Through the transformation of the closed-loop system with free matrices and the correspondent Lyapunov-Krasovskii functional, the delay-dependent stability condition of the closed-loop system is given. Then the parameterization of the controller is introduced, and a sufficient criterion for the solvability of the problem is obtained in terms of linear matrix inequality (LMI). When this LMI is feasible, an explicit expression of a desired dynamical output feedback controller is also given. A numerical example is given to demonstrate the proposed methods.