Filtering of Markovian Jump 2-D Systems

Abstract

This chapter considers the $\mathcal {H}_{\infty }$ filtering problem for Markovian jump 2-D systems. The mathematical model of Markovian jump 2-D 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 such filters are established in terms of LMIs, and the corresponding filter design is cast into a convex optimization problem which can be efficiently solved. In addition, the obtained results are further extended to more general cases where the system matrices also contain uncertain parameters. The most frequently used ways of dealing with parameter uncertainties, including polytopic and norm-bounded characterizations, are taken into consideration.