A novel Wirtinger-based inequality to \(H_\infty\) filtering for discrete-time systems with time-varying delay.

*(English)*Zbl 1435.93099Summary: This article is committed to \(H_{\infty}\) filtering for linear discrete-time systems with time-varying delay. The novelty of the paper comes from the consideration of the new Wirtinger-based inequality with double accumulation terms and the idea of delay-partitioning, which guarantees a better asymptotic stability and is less conservative than the celebrated free-weighting matrix or Jensen’s inequality methods. In combination with the improved Wirtinger-based inequality to handle the modified Lyapunov-Krasovskii (L-K) functionals, a new delay-dependent bound real lemma (BRL) is gained. In the light of the derived \(H_{\infty}\) performance analysis results, the \(H_{\infty}\) filter will be designed in response to linear matrix inequality (LMI). The validness of the proposed methods will be expressed via some numerical examples by the comparison of existing results.

##### MSC:

93C55 | Discrete-time control/observation systems |

26D15 | Inequalities for sums, series and integrals |

93B07 | Observability |

93B36 | \(H^\infty\)-control |

93C73 | Perturbations in control/observation systems |

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\textit{K. Ma} et al., Math. Probl. Eng. 2019, Article ID 5401734, 9 p. (2019; Zbl 1435.93099)

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