H ∞ control of singular systems via delta operator method

Abstract

This paper studies the problem of state feedback H ∞ control for singular systems through delta operator approach. A necessary and sufficient condition is presented such that a singular delta operator system is admissible with a prescribed H ∞ performance, which can provide a unified framework of the existing H ∞ performance analysis results for both continuous case and discrete case. The existence condition and explicit expression of a desirable H ∞ controller are also obtained for singular delta operator systems. The proposed design method can be used for both singular continuous systems and singular discrete systems directly. The corresponding design procedures, which simplify the classical approaches, are discussed and presented. All obtained conditions in this paper are in the form of strict linear matrix inequalities whose feasible solutions can be found by standard linear programming method. Numerical examples are provided to illustrate the effectiveness of the theoretical results obtained in this paper.