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

The three types of boundary value problem arising in singularly perturbed discrete control systems with two small parameters are considered. Each of these problems possesses three widely different clusters of eigenvalues, resulting in one slow mode and two stable or unstable fast modes and thereby exhibiting a three-time-scale character. Singular perturbation methods are developed to obtain approximate solutions in terms of an outer series solution and two boundary layer correction series solutions corresponding to the two small parameters. Three examples are given to illustrate the proposed methods for the three types of problem.