Fuzzy Arithmetic-based Stability Analysis and Design of Fuzzy Controller

Initially introduced as a model-free control design method, in today practice fuzzy control is dominantly used as yet another nonlinear control technique based either on a linear or nonlinear model of a process. This paper addresses the stability assessment of a fuzzy logic control system based only on the partial knowledge of a controlled process. Lyapunov stability conditions are derived and analyzed by using fuzzy numbers and fuzzy arithmetic. The experimental results obtained for a non-stable second-order system confirmed that this approach could be successfully implemented. Some questions, addressed in the paper, remained open for further investigation.