Singular perturbation method for initial value problems in two-parameter discrete control systems

Abstract

A singularly perturbed discrete control system with two small parameters is formulated as an initial value problem. The process of degeneration affects the corresponding two groups of initial conditions. A singular perturbation method is developed based on double asymptotic power series expansions where the approximate solution is sought in terms of an outer solution and two boundary layer correction solutions. Owing to the interplay between the various steps involved in the actual working of the method, an algorithm is presented. An example is provided to illustrate the proposed method.