On analysis of discrete singularly perturbed non-linear systems: Application to the study of stability properties

Recently we have introduced a model of singular perturbation for discrete-time non-linear systems. This paper is aimed at validating the proposed model. In fact, a discrete version of the well-known Tikhonovʹs theorem on singular perturbation of continuous-time systems is established. The second aim is to study stability problems of such systems. Sufficient conditions for both asymptotic and exponential stability are obtained. As a result, significant order reduction of stability problems is achieved. This is achieved by allowing a small parameter whose upper bound is estimated. Finally a simple example is given to illustrate the applications of the results.