Robust H_∞ Filtering for 2D Stochastic Systems

Abstract

This paper investigates the problem of H_∞ filter design for two-dimensional (2D) stochastic systems. The stochastic perturbation is first introduced into the well-known Fornasini-Marchesini local state-space model. Our attention is focused on the design of full-order and reduced-order filters, which guarantee the filtering error system to be mean-square asymptotically stable and to have a prescribed H_∞ disturbance attenuation performance. Sufficient conditions for the existence of such filters are established in terms of linear matrix inequalities, and the corresponding filter design is cast into a convex optimization problem, which can be efficiently handled by using available numerical software. 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. A numerical example is provided to illustrate the usefulness of the proposed filter design procedures.