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Network-based $$H_\infty$$ filtering using a logic jumping-like trigger. (English) Zbl 1319.93076
Summary: This paper is concerned with the network-based $$H_\infty$$ filtering for a stochastic system, where data transmission from the stochastic system to a filter is completed via a communication network. Network-induced delays, packet dropouts and packet disorders are unavoidable due to the use of the network. First, a logic zero-order-hold (ZOH) is designed to discard the disordered packets actively. The network-induced delays and packet dropouts are modeled as an interval time-varying delay. By decomposing the delay interval into $$N$$ subintervals uniformly, the filter to be designed is modeled as a Markov jumping filter with $$N$$ modes governed by a Markov chain. In order to work out the transition rate from one mode to another, a logic jumping-like trigger is embedded into the logic ZOH to simulate the switching of the Markov process. Second, based on the Markov jumping filter model together with a new integral inequality in the stochastic setting, a novel bounded real lemma is presented to ensure that the resultant filtering error system is mean exponentially stable with a prescribed $$H_\infty$$ performance. Then, a sufficient condition on the existence of desired Markov jumping filters is provided in terms of a set of linear matrix inequalities. Finally, an air vehicle system is employed to show effectiveness of the proposed design method.

##### MSC:
 93E11 Filtering in stochastic control theory 93B36 $$H^\infty$$-control
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