An LMI approach to exponential stabilization of uncertain time-delay systems

This paper presents a new, sufficient condition for exponential stabilization of uncertain systems with state-delays. By using a new Lyapunov function, the condition is obtained to be delay-dependent and represented in terms of linear matrix inequalities. Unlike some existing results on exponential stability and stabilization problems of time-delay systems, our condition involves information on the degree of exponential decay rates and therefore can suggest an achievable degree of speed of stabilization. Numerical examples are presented to show the effectiveness of the proposed method.