## Event-based $$H_\infty$$ filtering for sampled-data systems.(English)Zbl 1309.93096

Summary: This paper is concerned with event-based $$H_\infty$$ filtering for sampled-data systems. First, an event-based data packet processor is introduced to release sampled measurement outputs only if an event condition is violated. As a result, communication resources can be saved significantly while preserving the desired $$H_\infty$$ performance. Second, the resulting filtering error system is modeled as a system with an interval time-varying delay. By employing the Lyapunov-Krasovskii functional approach, a new Bounded Real Lemma (BRL) is established such that the filtering error system is asymptotically stable with the prescribed $$H_\infty$$ performance. Third, by performing an invertible linear transformation on the filtering error system, a Linear Matrix Inequality (LMI)-based sufficient condition, which is equivalent to the condition in the BRL, is obtained on the feasibility of the event-based $$H_\infty$$ filtering problem. Consequently, suitable $$H_\infty$$ filters and the event parameters in the event condition can be co-designed provided that a set of LMIs are satisfied. Finally, a mechanical system with two masses and two springs is given to show the effectiveness of the proposed method.

### MSC:

 93C57 Sampled-data control/observation systems 93E11 Filtering in stochastic control theory 93E10 Estimation and detection in stochastic control theory 93C65 Discrete event control/observation systems 93B36 $$H^\infty$$-control
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### References:

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