Delay-dependent stability of linear systems with delayed state: an LMI approach

This paper deals with the problem of asymptotic stability of a class of time-delay systems with constant, but unknown time-delay. Upper bounds on the time-delay that ensure the stability of the considered systems are given using a Razumikhin technique. Furthermore, the approach adopted here allows the computation of the delay bound by transforming the stability problem into an LMI optimization problem.