Nonlinear H∞ Filtering Based on Tensor Product Model Transformation

Abstract

The nonlinear $H_{\infty }$ filter design is always a desirable solution for nonlinear systems with noise of non-Gaussian or unknown distribution. This brief proposes a nonlinear $H_{\infty }$ filtering based on tensor product model transformation (TPMT), which is capable of transforming nonlinear systems to the conservativeness-reduced tensor product (TP) model through a polytopic linearization procedure. Both of the stable and unstable cases are considered, for which different linearization strategies and polytopic filters are specifically adopted. These filtering methods also incorporate the linearization error into design and can be formulated as linear matrix inequalities (LMIs) due to the polytopic feature from the resulted estimation error system so that they can be solved efficiently. Simulation results verify the effectiveness and robustness of the proposed filtering.