New stability criterion for a class of linear systems with time-varying delay and nonlinear perturbations

Abstract

The problem of robust stability for linear time-delay systems under nonlinear perturbations is discussed. The delay is assumed to be time-varying. A less conservative delay-dependent robust stability condition is derived by using some free matrices to express the relationship of the terms in the Leibniz–Newton formula within the framework of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed method.