Delay-dependent conditions for robust absolute stability of uncertain time-delay systems

This paper is concerned with the robust absolute stability analysis problem for a class of uncertain time-delay systems with nonlinearities satisfying a given sector condition. Based on the Lyapunov stability theory and the linear matrix inequality (LMI) approach, a delay-dependent sufficient condition for the robust absolute stability is derived and is expressed as the feasibility problem of a certain LMI system. A maximum upper bound of the allowable delay is obtained by solving a convex optimization problem. Finally, a numerical example is given to illustrate the proposed results.