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

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Abstract

This paper is concerned with output feedback stabilization of discrete-time Takagi-Sugeno fuzzy systems with immeasurable premise variables. Takagi-Sugeno fuzzy systems can usually approximate nonlinear systems and even describe a certain class of nonlinear system exactly. When we consider 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 its fuzzy system description is difficult. In this paper, we consider the output feedback stabilization problem. In this problem, the premise variable may not be unknown. Thus we formulate the output feedback stabilization problem of fuzzy systems as robust stabilization of uncertain systems. Numerical examples illustrate our theory.

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