Ein Ansatz zur Stabilitätsanalyse und Synthese von Fuzzy-Regelungen

The design of fuzzy controllers often appears as a trial and error method. To change this heuristic approach to a more analytic one for analysis and design of systems governed by fuzzy controllers, we propose the application of some methods for stability analysis. As fuzzy controllers usually represent a nonlinear mapping from input to output signals, some well known criteria based on nonlinear control theory are used. The Popov-criterion turns out to be quite simple for this purpose, however it is subject to strong restrictions. Using Lyapunov-theory the design of Lyapunov-functions is provided by the method of M. A. Aizermann, which can be applied to a wider range of systems. This method is primarily developed for computer aided analysis