D-stability bound analysis for discrete multiparameter singularly perturbed systems

The D-stability (i.e., the stability in the sense that all the poles of a system are lying inside the disk D(α, r)) problem for discrete multiparameter singularly perturbed systems is considered in this brief. A two-stage method is first developed to analyze the stability relationship between the discrete multiparameter singularly perturbed systems and their corresponding reduced systems. An upper bound of the singular perturbation parameters is then derived such that the D-stability of the reduced systems implies that of the original systems, provided that the singular perturbation parameters are small enough to be within this bound. This fact enables us to investigate D-stability of the original systems by establishing that of their corresponding reduced systems.