A novel approach to stability of interval delayed systems with nonlinear perturbations

Abstract

Thispaper focuses on the stability problem for a class of linear systems withinterval time-varying delays and nonlinear perturbations. By developing a delaydecomposition approach, the information of the delayed plant states can betaken into full consideration in a newLyapunov-Krasovskii (LK)functional, and a delay-fractional-dependent sufficient stability criterion isobtained in terms of linear matrix inequalities without involving any directapproximation in the time-derivative of the LKfunctional. The merits of the proposed results lie in their less conservatism,which are realized by choosing different Lyapunovmatrices in the decomposed integral intervals andutilizing some suitable integral inequalities to estimate some tighter upperbounds in some cross terms more exactly. This development leads to a lessconservative LMI criterion as seen through numerical examples.