Asymptotic stability of linear systems with multiple time-invariant state-delays

Abstract

In this paper, we investigate the asymptotic stability of the linear systems with multiple time-invariant delays. The delay elements are removed from the original system by using a parameter-dependent Padé approximation, resulting in a delay-free comparison system with real parameter uncertainties. We then show that, the robust stability of the comparison system, not only ensures the asymptotic stability of the original time-delay system, but also guarantees an a priori upper bound on the degree of conservatism which only depends on the order of the Padé approximation used. Finally, we present a new, delay-dependent condition, formulated in terms of Linear Matrix Inequalities, for the asymptotic stability of the time-delay systems.