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A delay decomposition approach to $$H_\infty$$ admissibility for discrete-time singular delay systems. (English) Zbl 1354.93048
Summary: This paper considers the problem of delay-dependent admissibility condition and $$H_\infty$$ performance analysis for discrete-time singular delay systems. By utilizing the delay decomposition approach, an improved delay-dependent admissibility condition is presented in terms of linear matrix inequalities (LMIs). This admissibility condition is much less conservative than some existing results and includes those as its special cases. Based on the proposed condition, a new delay-dependent bounded real lemma is also given, which guarantees the admissibility and the $$H_\infty$$ performance. Numerical examples are given to illustrate the effectiveness of the proposed method.

##### MSC:
 93B36 $$H^\infty$$-control
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