H∞ Controller Design via State Feedback for Uncertain Discrete-time Singularly Perturbed Systems

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