H∞H∞ control for fast sampling discrete-time singularly perturbed systems

This paper is concerned with the H∞H∞ control problem via state feedback for fast sampling discrete-time singularly perturbed systems. A new H∞H∞ controller design method is given in terms of solutions to linear matrix inequalities (LMIs), which eliminates the regularity restrictions attached to the Riccati-based solution. A method for evaluating the upper bound of singular perturbation parameter ϵϵ with meeting a prescribed H∞H∞ performance bound requirement is also given. Furthermore, the results are extended to robust controller design for fast sampling discrete-time singularly perturbed systems with polytopic uncertainties. Numerical examples are given to illustrate the validity of the proposed methods.