Exponential stability and stabilization of linear systems with time varying delays

This paper deals with a problem of exponential delay dependent stability and stabilization of linear systems with time varying delays. Using the Lyapunov parameter dependent functional, new sufficient conditions for exponential stability criterion has been derived in terms of linear matrix inequalities (LMIs) which can be easily solved using efficient convex optimization algorithms. Hence, the allowable upper bound of time delay system can be easily estimated with respect to the delay decay rate. Based on these results, the state feedback stability problem is solved. Numerical examples are carried out to support the applicability of the proposed method and the effectiveness of our results.