Stability of linear time-varying delay systems and applications to control problems

Abstract

This paper deals with the stability of a class of linear time-varying systems with multiple delays. Using the Lyapunov function method, we give sufficient delay-dependent conditions for the exponential stability with a given convergence rate, which are described in terms of linear matrix inequalities (LMI) and the solution of Riccati differential equations (RDE). The results are applied to the problem of stabilization of linear time-varying control systems with multiple delays. Numerical examples are given to illustrate the results.