Robust H∞1 control for standard discrete-time singularly perturbed systems

The state feedback Hinfin control problem for standard discrete-time singularly perturbed systems with polytopic uncertainties is considered. Two methods for designing Hinfin controllers are given in terms of solutions to a set of linear matrix inequalities, where one of them is with the consideration of improving the upper bound of singular perturbation parameter e. Moreover, a method of evaluating the upper bound of singular perturbation parameter e with meeting a prescribed Hinfin performance bound requirement is also given. Numerical examples are given to illustrate the effectiveness of the proposed methods.