On the robust stability of interval time-delay systems – An application of the upper solution bounds of the Lyapunov equation

In this paper, the robust stability test problem of the interval time-delay systems is discussed. We first study the upper solution bounds of the continuous algebraic Lyapunov equation (the CALE). By using linear algebraic techniques, a simple approach is proposed to derive new upper bounds of the CALE. Compared to existing works on this topic, these newly obtained bounds are less restrictive and easier to calculate. Then, we apply them to solve the mentioned problem. By using Lyapunov equation approach associated with these upper bounds, new concise criteria for the robust stability and decay rate test problem of the mentioned systems are presented. Comparing to some well-known results of the time-delay systems, the obtained criteria are sharper. An interesting consequence of these results is that it is not necessary to solve any Lyapunov equation although the Lyapunov equation approach is used.