On improved delay-range-dependent stability condition for linear systems with time-varying delay via Wirtinger inequality

Abstract

This paper studies the problem of delay-range-dependent stability analysis for the continuous-time linear systems with time-varying delay. A new and appropriate Lyapunov–Krasovskii (L–K) functional is constructed. To estimate the quadratic integral terms coming out from the derivative of L–K functional, utilize the well-known Wirtinger integral inequality together with the reciprocal convex lemma. Then, an improved delay-range-dependent stability condition is being established in terms of linear matrix inequalities (LMIs) in such a way that it can be effectively solved by using existing software (LMI toolbox in MATLAB). The delay upper bound results obtained by the developed stability condition are found to be less conservative than other recent results. Furthermore, the proposed stability criterion use the less number of decision variables and give the consistent delay bound results compared to some other methods. Two numerical examples are given to illustrate the effectiveness of the obtained stability condition compared to some recently published stability methods.