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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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