ℋ∞ filter design for nonlinear polynomial systems

The problem of ℋ∞ filter design for continuous-time nonlinear polynomial systems is addressed in this paper. The aim is to design a full order dynamic filter that depends polynomially on the filter states. The strategy relies on the use of a quadratic Lyapunov function and an inequality condition that assures an ℋ∞ performance bound for the augmented polynomial system, composed by the original system and the filter to be designed, in a regional (local) context. Then, by using Finsler's lemma, an enlarged parameter space is created, where the Lyapunov matrix appears separated from the system matrices in the conditions. Imposing structural constraints to the decision variables and fixing some values for a scalar parameter, design conditions for the ℋ∞ filter can be obtained in terms of linear matrix inequalities. As illustrated by numerical experiments, the proposed conditions can improve the ℋ∞ performance provided by standard linear filtering by including the polynomial terms in the filter dynamics.