Robust stability of non-standard nonlinear singularly perturbed discrete systems with uncertainties

Abstract

In the past several decades, the singularly perturbed discrete systems have received much attention for the stability analysis and controller design. Recently, there are some results about the nonlinear singularly perturbed discrete systems. Compared with the existing result, we consider the robust stability of the uncertain nonlinear singularly perturbed discrete systems with the less conservative assumption via the Lyapunov function method. Moreover, the previous results of the singularly perturbed discrete system are only applied to the system, which is composed of the slow part and the fast part, separately. However, we consider the non-standard nonlinear singularly perturbed discrete system in which the slow part and the fast part coexist, that is, a general case of the nonlinear singularly perturbed discrete systems. Then, by using the lower-order subsystems from two standard systems, we present the robust stability of the non-standard nonlinear singularly perturbed discrete system with uncertainties.