Special Issue "Fuzzy/Neural Network Applications to Dynamics and Control of Mechanical Systems". Stability Analysis of Fuzzy Systems and Construction Procedure for Lyapunov Functions.
Kazuo A. TANAKA, Michio Sugeno · TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series C · 1992
The stability analysis of fuzzy systems is discussed in accordance with the definition of stability in the sense of Lyapunov. The main disadvantage of Lyapunov's stability criterion is that it gives only the sufficient conditions for stability, not the necessary conditions. Furthermore, there are no unique methods of determining Lyapunov functions for a wide class of systems. The purpose of this paper is to propose a construction procedure of Lyapunov functions for a class of fuzzy systems. First, we discuss stability analysis of fuzzy systems using Lyapunov's direct method. A sufficient for ensuring stability of fuzzy systems is obtained. Secondly, two conditions which are used for finding Lyapunov functions are derived : a necessary condition and a ncessary and sufficient condition for ensuring existence of Lyapunov functions. Finally, the effectiveness of this procedure is verified by some examples.