Nonlinear H2 Filtering Based on Tensor Product Model Transformation for Nonlinear Discrete System

For the nonlinear discrete systems with strong nonlinearity and large initial error, conventional nonlinear filtering methods get degraded due to the local linearization error, heavy calculation burden and divergence. In this paper, the tensor product H
₂
(TPH
₂
) filter method is proposed based on the global polytopic linearization. Firstly, the nonlinear system is transformed to the polytopic linearization model by the tensor product model transformation (TPMT), which features as a numerical method. To obtain the exact nonlinear system tensor product (TP) model, the conservativeness of the TP model is effectively reduced through the optimal correction algorithm. Secondly, the corresponding polytopic TPH
₂
filter model is designed with the unknown filter gain. The resultant polytopic filter error system model is calculated by combining the nonlinear discrete system with the polytopic filter model. Finally, the TPH
₂
filter method is finalized to obtain the filter gain and the H
₂
norm. The parameter dependent polytopic matrix inequalities in the TPH
₂
filter method can be solved by converting to a group of linear matrix inequalities (LMI). Numerical simulations are provided to demonstrate the effectiveness and feasibility of the method.