Robust stability analysis of discrete time-delay systems subjected to nonlinear uncertainties

In this paper, the problem of robust stability analysis for discrete time-delay systems subjected to nonlinear norm-bounded uncertainties is addressed. By using Lyapunov stability theorem associated with a simple matrix bound of the solution of the discrete Lyapunov equation, a delay-independent criterion is presented to guarantee the robust stability of the mentioned systems. This approach is then applied to discuss the same problem for time-delay systems without uncertainties. A sufficient condition is also obtained. Compared to what has appeared in the literature to date, the proposed condition is sharper. The feature of these obtained criteria is that they do not need to solve any Lyapunov equation, although the Lyapunov equation approach is adopted.