H ∞ 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 filter 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 scalar 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 quadratic terms in the filter dynamics.