Robust Output Feedback Stabilization of Uncertain Discrete-Time Fuzzy Systems with Immeasurable Premise Variables

Abstract

This paper is concerned with robust output feedback stabilization of uncertain discrete-time Takagi-Sugeno fuzzy systems with immeasurable premise variables. When we consider Takagi-Sugeno fuzzy systems, the selection of premise variables plays an important role. The premise variables are usually given, and so the output is selected as the premise variable. In this case, however, a fuzzy system description is limited. If the premise variable is the state of the system, then a fuzzy system describes a wide class of nonlinear systems. In this case, a controller design based on parallel distributed compensation is impossible because the controller depends on immeasurable premise variables. In this paper, we consider the robust output feedback stabilization problem for uncertain fuzzy systems where the premise variable is the state, which is not measurable. We formulate such a problem as a robust stabilization problem of uncertain linear systems. Some numerical examples illustrate our theory.