Improved stability and H performance criteria for linear systems with interval time-varying delays via three terms approximation

This paper investigates the problem of delay dependent stability and H∞ performance for a class of linear systems with interval time-varying delay. A new model transformation is first proposed by employing a three-terms approximation of delayed state variables, for a better approximation of delayed state. By using scaled small gain theorem and a simple Lyapunov–Krasovskii functional, new stability and H∞ performance criteria are proposed in terms of linear matrix inequalities, which can be easily solved by using standard numerical packages. Finally, numerical examples are presented to illustrate the effectiveness of the proposed method.