Stability of perturbed systems with time-varying delays

Abstract

This paper gives easily verifiable sufficient conditions of robust asymptotic stability of linear time-delay systems subject to parametric unstructured or highly-structured perturbations. The criteria given in this paper are delay-independent or delay-dependent. The considered delay may be time-varying. An estimation of the transient behaviour of the studied systems is also provided (exponential rate of convergence). Scalar or vectorial inequalities involving Hurwitz matrices, matrix measures and norms constitute the mathematical foundations of the exposed results.