H∞ filtering for fuzzy systems with immeasurable premise variables: An uncertain system approach

This paper discusses a design of stable filters with H∞ disturbance attenuation of Takagi–Sugeno fuzzy systems with immeasurable premise variables. When we consider the filter design of Takagi–Sugeno fuzzy systems, the selection of premise variables plays an important role. If the premise variable is the state of the system, then a fuzzy system describes a wide class of nonlinear systems. In this case, however, a filter design of fuzzy systems based on parallel distributed compensator idea is infeasible. To avoid such a difficulty, we consider the premise variables uncertainties. Then we consider a robust H∞ filtering problem for such an uncertain system. A solution of the problem is given in terms of linear matrix inequalities (LMIs). Some numerical examples are given to illustrate our theory.