New delay-dependent stability criteria for linear systems with multiple time-varying delays

Abstract

For systems with a delay varying in an interval studied by Shao (New delay-dependent stability criteria for systems with interval delay. Automatica, 45 (2009) 744-749) a tight upper bound on its derivative of different Lyapunov functional has been suggested, but this method is not suited to systems with multiple varying delays. Before proving the main theorem, a more generalized convex combination inequality is proposed. A new stability criterion for systems with multiple time-varying delays is obtained in this paper by the general inequality technique. Two examples are included to illustrate the effectiveness of the presented results.