Robust Guaranteed Cost Filtering for a Class of Nonlinear Systems

In this paper, we propose a deterministic approach to the robust filtering problem for a class of uncertain nonlinear systems. Based on polynomial Lyapunov functions and a relaxation technique, we derive linear matrix inequalities conditions that minimize an upper-bound on the finite horizon 2-norm of the estimation error for all admissible uncertainty and input signals (including disturbances and measurement noise). Through a simple redefinition of the Lyapunov matrix, we extended the results for the reduced-order case without considering non-convex rank constraints.