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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 theory |

60J75 | Jump processes (MSC2010) |

15A39 | Linear inequalities of matrices |

### Keywords:

Markovian jump linear systems; \(H_\infty \) filtering; partly unknown transition probabilities; linear matrix inequality (LMI)
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\textit{L. Zhang} and \textit{E.-K. Boukas}, Automatica 45, No. 6, 1462--1467 (2009; Zbl 1166.93378)

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### References:

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