Improved Robust H∞ Filtering Approach for Nonlinear Systems

An improved design approach of robust H∞ filter for a class of nonlinear systems described by the Takagi‐Sugeno (T‐S) fuzzy model is considered. By introducing a free matrix variable, a new sufficient condition for the existence of robust H∞ filter is derived. This condition guarantees that the filtering error system is robustly asymptotically stable and a prescribed H∞ performance is satisfied for all admissible uncertainties. Particularly, the solution of filter parameters which are independent of the Lyapunov matrix can be transformed into a feasibility problem in terms of linear matrix inequalities (LMIs). Finally, a numerical example illustrates that the proposed filter design procedure is effective.