Delay-dependent robust control for discrete-time uncertain singular systems with interval time-varying delays in state and control input

The problem of the delay-dependent robust H ∞ controller design for discrete-time uncertain singular systems with interval time-varying delays in state and control input is investigated in this paper. A new delay-dependent bounded real lemma for singular systems with interval time-varying delays is derived and expressed in terms of LMI. Based on the result, the controller existence condition and robust H ∞ state feedback controller design method are proposed by linear matrix inequality (LMI) approach without any decompositions of system matrices and equivalent transformation. Also, the resulting criterion is extended to delayed discrete-time singular systems with polytopic uncertainties. Numerical examples are presented to demonstrate the effectiveness of the proposed method.