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A novel Wirtinger-based inequality to $$H_\infty$$ filtering for discrete-time systems with time-varying delay. (English) Zbl 1435.93099
Summary: 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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