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Mode-dependent ${H}_{\infty }$ filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities. (English) Zbl 1166.93378
Summary: The problem of ${H}_{\infty }$ filtering for a class of discrete-time Markovian Jump Linear Systems (MJLS) with partly unknown transition probabilities is investigated. The considered systems are more general, which cover the MJLS with completely known and completely unknown transition probabilities as two special cases. A mode-dependent full-order filter is constructed and the Bounded Real Lemma (BRL) for the resulting filtering error system is derived via LMI formulation. Then, an improved version of the BRL is further given by introducing additional slack matrix variables to eliminate the cross coupling between system matrices and Lyapunov matrices among different operation modes. Finally, the existence criterion of the desired filter is obtained such that the corresponding filtering error system is stochastically stable with a guaranteed ${H}_{\infty }$ performance index. A numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results.
##### MSC:
 93E11 Filtering in stochastic control 60J75 Jump processes 15A39 Linear inequalities of matrices