## Delay-dependent robust $$H_\infty$$ controller synthesis for discrete singular delay systems.(English)Zbl 1237.93054

Summary: The problems of delay-dependent robust stability analysis, robust stabilization and robust $$H_{\infty }$$ control are investigated for uncertain discrete-time singular systems with state delay. First, by making use of the delay partitioning technique, a new delay-dependent criterion is given to ensure the nominal system to be regular, causal and stable. This new criterion is further extended to singular systems with both delay and parameter uncertainties. Then, without the assumption that the considered systems being regular and causal, robust controllers are designed for discrete-time singular time-delay systems such that the closed-loop systems have the characteristics of regularity, causality and asymptotic stability. Moreover, the problem of robust $$H_{\infty }$$ control is solved following a similar line. The obtained results are dependent not only on the delay, but also on the partitioning size and the conservatism is non-increasing with reducing partitioning size. These results are shown, via extensive numerical examples, to be much less conservative than the existing results in the literature.

### MSC:

 93B50 Synthesis problems 93D09 Robust stability 93C55 Discrete-time control/observation systems
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