A simple stability condition and decay rate estimation of time-delay systems

By using Lyapunov equation approach associated with some linear algebraic techniques, new simple criteria for the robust stability and decay rate test problem of the time-delay systems are proposed. Comparing to well-known results, the presented criteria are sharper. The presented schemes then are applied to solve the mentioned problems for uncertain time-delay systems. Delay-dependent and delay-independent conditions for the robust stability and decay rate test are also developed. An interesting consequence of these results is that it is not necessary to solve any Lyapunov equation although the Lyapunov equation approach is used. Numerical examples are also given to compare the tightness of the presented results and some appeared in the literature.