Abstract:
Ｈ∞ analysis for descriptor discrete systems with multi-time delay is considered. By means of linear matrix inequalities, it is proved that a sufficient condition for the system to have the general γ-suboptimal Ｈ∞ performance is that there exist a symmetric and invertible matrix Ｐ and positive definite matrices Ｓｉ（ｉ＝１，…，Ｎ）satisfying some conditions. Furthermore, the general bounded real lemma (GBRL) for descriptor discrete systems is extended to the system with multi-time delay. Finally, it is proved that a sufficient condition for the corresponding normal system to have γ-suboptimal Ｈ∞ performance is that there exist symmetric and invertible matrix Ｐ and positive definite matrices Ｓｉ（ｉ＝１，…，Ｎ） satisfying certain conditions. And a numerical example is presented to illustrate the efficiency of our results.
