Stability of linear systems with delayed perturbations: an LMI approach

For a class of linear systems with time-varying perturbations in the time-delayed state, this paper presents a couple of new sufficient conditions for guaranteeing asymptotic stability. Since these conditions can be expressed as linear matrix inequalities (LMIs), the corresponding LMI-based algorithms for determining stability bounds are derived. Furthermore, we extend these results to linear systems with multiple time-varying perturbations in time-delayed states and those with structured time-varying perturbations in time-delayed states. Compared with existing results, our methods are shown to be superior. Numerical examples are given to demonstrate the effectiveness of the proposed approaches.