H_∞ polytopic filter design for nonlinear systems

This paper proposes an H_∞ polytopic filter design for a nonlinear system. Based on the polytopic approximation of the nonlinear system, the polytopic filter design is converted into a group of linear matrix inequalities (LMIs) so that the polytopic filter parameters can be effectively acquired by numerical convex optimization algorithms. At this stage, the tensor product (TP) model transformation is utilized to compute the polytopic approximation of the nonlinear system. Particularly, a new rectification procedure is further developed to obtain a specific polytopic approximation with all the vertex systems being stable, which premises the solvability of the LMIs. The method is much easier to be implemented than traditional approaches such as the Hamilton-Jacobi inequality (HJI)-based methods. Simulation demonstrates the method is much less conservative than the existing method and has good estimation performance.