On State Feedback H∞ Control for Discrete-Time Singular Systems

This technical note deals with the state feedback H_∞ control problem for linear time-invariant discrete-time singular systems. Relied on the use of auxiliary matrices and a positive scalar, a novel necessary and sufficient condition for the bounded real lemma is derived for discrete-time singular systems. The characterization is reduced to a strict linear matrix inequality (LMI) when the scalar is fixed, and the resulting LMI is non-conservative as long as the scalar is chosen sufficiently large. Moreover, the result is further expanded to H_∞ controller design, and a numerically efficient and reliable design procedure is given. Since no particular restriction is imposed on the auxiliary matrices, the proposed result outperforms the existing methods in the literature. Numerical examples are included to illustrate the effectiveness of the present result.