Robust stability analysis for time-delay systems using the integral quadratic constraint approach

Given a time-delay system, we are interested in finding new robust stability conditions for the system. We apply the integral quadratic constraint approach to obtain two results which allow us to test the robust stability using the linear matrix inequality technique. Both results give an estimate of the maximum time-delay which preserves robust stability. The first result is simpler to apply while the second one gives a less conservative robust stability condition.