Central suboptimal H∞ filter design for nonlinear polynomial systems with multiplicative noise

This paper presents the central finite-dimensional H∞ filter for nonlinear polynomial systems, that is suboptimal for a given threshold γ with respect to a modified BolzaMeyer 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 designs the central suboptimal H∞ filter for the general case of nonlinear polynomial systems, based on the optimal H2 filter given in [24]. 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∞ filter available for the corresponding linearized system.