H∞ output feedback control for fuzzy systems with immeasurable premise variables: Discrete-time case

This paper discusses H∞ output feedback control of discrete-time Takagi-Sugeno fuzzy systems with immeasurable premise variables. When we consider the output feedback control 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. However, the state is not measurable in the output feedback control problem. In this case, a control design of the underlying nonlinear system based on parallel distributed compensation is infeasible because a controller depends on the immeasurable state variable. In this paper, we introduce a new method to treat fuzzy systems with immeasurable premise variables and consider a design method of H∞ output feedback control problem. We formulate this fuzzy control problem as a robust H∞ control of an uncertain system. Numerical examples are given to illustrate our methods.