An approach to stability analysis for fuzzy control systems with parametric uncertainty

In order to analysis the stability of a class of time invariant, single value nonlinear control systems quantitatively, stability margins of self-sustaining oscillation was defined, and self-sustained oscillation criterion is proposed, by extending the stability margins of linear system in frequency domain to the harmonic balance method of nonlinear system. Two typical fuzzy control systems with strong application background have been analyzed by applying the method successfully, where the time-varying properties of the object is represented by parameters uncertainty. The simulation results verify the effectiveness of the method. The advantage is prominent for fuzzy control systems since the fuzzy rules are difficultly expressed by equations. Through, our method, we could look into the time domain behaviors of nonlinear control systems from their stability margins of self-sustaining oscillation in frequency domain. Further more, it could help us to explain why self-sustaining oscillation occurs in physical equipment and how to avoid it.