## $$\mathcal H_{\infty}$$ filtering for 2D Markovian jump systems.(English)Zbl 1149.93346

Summary: This paper is concerned with the problem of $$\mathcal H_{\infty}$$ 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 $$\mathcal H_{\infty}$$ 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 theory 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 93E03 Stochastic systems in control theory (general)
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### References:

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