The problem of H∞ control of discrete-time singularly perturbed systems is studied. A method of evaluating the upper bound of singular perturbation parameter ε is given in terms of linear matrix inequalities. A sufficient condition on searching for the allowable upper bound ε* is obtained, so that the discrete-time singularly perturbed system is asymptotically stable and satisfies a prescribed H∞ norm bound for any singular perturbation parameter ε∈(0,ε*］. A numerical example is given to illustrate the effectiveness of the proposed method.

singularly perturbed system; linear matrix inequality; H∞ control; discrete-time