H∞ control of singular systems via delta operator approach

This paper investigates the problem of state feedback H_∞ control for singular systems through delta operator approach. Firstly, a bounded real lemma corresponding to a singular continuous system under the framework of the delta operator model is obtained. Then, the existence condition and explicit expression of a desirable H_∞ controller for the singular delta operator system are presented. As special cases, the results of admissible control for the singular delta operator system and H_∞ control as well as admissible control for the singular continuous system are also derived. All required conditions in this paper are characterized in the form of strict linear matrix inequalities whose feasible solutions can be obtained easily and directly. Finally, some numerical examples are provided to illustrate the effectiveness of the obtained theoretical results in the paper.