Robust stability of linear systems with delayed perturbations

Abstract

In this paper, a new sufficient delay independent robust stability condition is introduced for a class of linear systems with unstructured time-varying delayed perturbations. The stability condition is formulated in terms of the solution of a Lyapunov equation. Since this method needs the tuning of a positive definite symmetric matrix for which there is no any tuning procedure, the stability condition is also given in a solvable linear matrix inequalities (LMI) form. The LMI formulation does not require the tuning of any parameter. The result based on the solution of a Lyapunov equation is analytically shown that the robust stability bound is invariant when a system and its dual system with constant delay time are considered. A numerical example is given for the computation of the robust stability bound. A brief comparison with the previously reported results is also presented.