Robust \(H_\infty\) filtering for 2D stochastic system
The paper deals with the \(H_{\infty}\) filtering problem for an extended Fornasini-Marchesini local state-space model, established by introducing stochastic perturbations, which are governed by a white-noise signal and cause the system matrices to fluctuate above their deterministic nominal values. The design concerns the full-order and reduced-order filters, which guarantee the mean-square asymptotic stability of filtering error system and a prescribed \(H_{\infty}\) disturbance attenuation performance. Sufficient existence conditions in terms of linear matrix inequalities are derived and it is shown that for the filter design a convex optimization procedure can be performed. Extensions to more general cases where the system matrices contain uncertain parameters are provided, by including polytopic and norm-bounded characterizations in order to deal with parameter uncertainties. Finally a numerical example illustrates the usefulness of the proposed filter design procedures.
scientific article; zbMATH DE number 2152923