Stability Analysis of Uncertain Nonlinear Singularly Perturbed Discrete Systems

In this paper, the robust stability of uncertain nonlinear singularly perturbed discrete systems is considered via the Lyapunov function method. We decompose the uncertain nonlinear singularly perturbed discrete system into the slow subsystem and the fast subsystem based on the manifold from the slow dynamics. Then, the stability conditions of the slow subsystem and the fast subsystem are obtained, respectively. The stability conditions of the slow subsystem and the fast subsystem guarantee the robust stability of the uncertain nonlinear singularly perturbed discrete system through the composite Lyapunov function. Finally, we show an illustrative example in order to show the validity of our result. Keywords-Singular perturbation; Discrete-time system; Lyapunov method; Robust stability;