On mutiparameter singularly perturbed discrete-time systems

This note considers discrete-time systems with several small singular perturbation parameters. The aim is to explore analogies with the (continuous-time) multiparameter singular perturbation theory. The models considered are obtained first as discretizations of continuous-time multiparameter singularly perturbed systems, and then noted to be natural extensions of standard discrete-time single parameter singular perturbation problems. Particular attention is paid to the stability characteristics of the new models. The conclusions reached on this issue lead to the suggestion of more exotic multiparameter discrete-time models due to the richer stability properties which can be achieved.