Delay-dependent robust stabilization of linear time-delay uncertain systems

The delay-dependent robust stabilization of an uncertain linear system with both state and input delays was discussed. By combining the matrix decomposition idea with the Lyapunov-Krasovskii functional method, adding an appropriate zero term to the deviation of V, and introducing a free weight matrix, a delay-dependent sufficient condition based on linear matrix inequality was derived to ensure the system's robust stabilization via memoryless state feedback, and a specified controller design method was proposed. A numerical example was given to illustrate that the new results were less conservative than the present literatures.