Optimization approach to the robustness of linear delay systems

By using the Lyapunov equation approach and an improved Razumikhin-type theorem, this paper presents a new robust stability criterion for a linear system subject to delayed time-varying nonlinear perturbations. Then, by using a parameter optimization technique, an efficient algorithm is derived for determining a desirable matrix for the Lyapunov equation. As a consequence, less conservative robust stability bounds for the perturbed system are achieved. Numerical examples are included to demonstrate the effectiveness of the proposed approach.