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Zbl 1149.93346
Wu, Ligang; Shi, Peng; Gao, Huijun; Wang, Changhong
$\cal H_{\infty}$ filtering for 2D Markovian jump systems. (English)
[J] Automatica 44, No. 7, 1849-1858 (2008). ISSN 0005-1098

Summary: This paper is concerned with the problem of $\cal H_{\infty}$ filtering for 2D discrete Markovian jump systems. The mathematical model of 2D jump systems is established upon the well-known Roesser model. Our attention is focused on the design of a full-order filter, which guarantees the filtering error system to be mean-square asymptotically stable and has a prescribed $\cal H_{\infty}$ disturbance attenuation performance. Sufficient conditions for the existence of a desired filter are established in terms of linear matrix inequalities, and the corresponding filter design is cast into a convex optimization problem which can be efficiently solved by using commercially available numerical software. A numerical example is provided to illustrate the effectiveness of the proposed design method.

MSC 2000:: *93E11 Filtering in stochastic control
60J10 Markov chains with discrete parameter
93E03 General theory of stochastic systems

Keywords: linear matrix inequality (LMI); Markovian jump linear systems (MJLS); $\cal H_{\infty}$ filtering; 2D systems

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Zentralblatt MATH Berlin [Germany]