Stability robustness analysis of linear systems with delayed perturbations

This paper focuses on the problem of robust stability analysis of systems with delayed time-varying perturbations. A necessary and sufficient condition for the robust quadratic stability is derived. Based on that, a convex optimization problem is formulated to find the bounds on allowable perturbations which maintain the stability of the perturbed system. These bounds are shown to be less conservative than the existing ones. Numerical examples are given to illustrate the results.