Central suboptimal H∞ filtering for nonlinear polynomial systems with multiplicative noise

Abstract

This paper presents the central finite-dimensional H∞ filter for nonlinear polynomial systems with multiplicative noise, that is suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the paper reduces the original H∞ filtering problem to the corresponding optimal H2 filtering problem, using the technique proposed in [1]. The paper presents the central suboptimal H∞ filter for the general case of nonlinear polynomial systems with multiplicative noise, based on the optimal H2 filter given in [31]. The central suboptimal H∞ filter is also derived in a closed finite-dimensional form for third (and less) degree polynomial system states. Numerical simulations are conducted to verify performance of the designed central suboptimal filter for nonlinear polynomial systems against the central suboptimal H∞ filters available for polynomial systems with state-independent noise and the corresponding linearized system.