Central suboptimal H∞ filter design for nonlinear polynomial systems

This paper presents the central finite-dimensional H_infin filter for nonlinear polynomial systems, that is suboptimal for a given threshold gamma 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_infin filtering problem to the corresponding optimal H₂ filtering problem, using the technique proposed. The paper designs the central suboptimal H_infin filter for the general case of nonlinear polynomial systems, based on the optimal H₂ filter given. The central suboptimal H_infin 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_infin filter available for the corresponding linearized system.