Delay-dependent robust stability criteria for linear systems with interval time-varying delays and nonlinear perturbations

Abstract

This paper studies delay-dependent robust stability criteria for linear systems with interval time-varying delays and nonlinear perturbations. Nonlinear perturbations and norm-bounded uncertainties are considered. The constraint on the derivative of the time-varying delay is not required which allows the time-delay to be a fast time-varying function. Based on the Lyapunov-Krasovskii theory, we derive new delay-dependent stability conditions in terms of linear matrix inequalities (LMIs) which can be solved by various available algorithms. The new stability condition is much less conservative and is more general than some existing results. Numerical examples are given to illustrate the effectiveness of our theoretical results.