Gain-scheduled H∞ admissibilisation of LPV discrete-time systems with LPV singular descriptor

This paper deals with the admissibilisation with guaranteed H-infinity performance of linear parameter-varying (LPV) discrete-time singular systems under gain-scheduled (GS) state-feedback control. In particular, we focus on systems with descriptor matrix of LPV form and unknown/unmeasurable disturbance input. To our best knowledge and despite its practical interest, this problem has not been fully investigated and still poses relevant issues, which motivates our study. By means of a proposed descriptor redundancy approach, in combination with the bounded real lemma and Finsler's Lemma, a method based on linear matrix inequalities is proposed to design a GS state-feedback control with maximum H performance. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.