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$\cal H_{\infty}$ filtering for 2D Markovian jump systems. (English) Zbl 1149.93346
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:
 93E11 Filtering in stochastic control 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 93E03 General theory of stochastic systems
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##### References:
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