H-Infinity Filter Design for Nonlinear Quadratic Systems

Abstract

This paper is concerned with the problem of H∞ filtering for continuous-time nonlinear quadratic systems. The aim is to design a full order dynamic fi lter that can also contain quadratic terms. The strategy relies on the use of a quadratic Lyapunov function and an inequality condition that assures an H∞ performance bound for the augmented quadratic system, composed by the original system and the filter to be designed, in a regional (local) context. Then , by using the Finsler's lemma, an enlarged parameter space is created, where the Lyapunov matrix appears separated from the system matrices. Imposing structural constraints to the decision variables , theoretical conditions, which can be treated as linear matrix inequality conditions by fixing a grid on a sc alar parameter, can be derived for the filter design. As illustrated by numerical experiments, the proposed conditions can improve the H∞ performance provided by linear filters by including the quad ratic terms in the filter dynamics.