Less conservative delay-dependent robust stability criteria for linear time-delay systems

In this paper, delay-dependent stability problem of linear systems is considered. A new Lyapunov-Krasovskii functional is constructed and Jensen´s inequality is applied to the cross terms. The proposed method is then extended to the case of uncertain polytopic systems. All the conditions are given in terms of linear matrix inequalities that are efficient to solve and no slack matrix variable is introduced. Some numerical examples are provided to illustrate the effectiveness and less conservativeness of our method.