Absolute Stability Analysis and Design of Fuzzy Control Systems

This paper investigates the sufficient conditions under which a fuzzy control system is absolutely stable based on the absolute stability theory, and proposes a new design method for fuzzy control systems. First, a PD type fuzzy control system is transformed into a Lurie system with two nonlinear parts. Then, we build the state-space representation of this Lurie system. Next, by applying absolute stability theory, the sufficient conditions are explored under which the system is stable, that is, the output control signals of the system are non-linear with sector constraints. Furthermore, a novel method based these conditions for the design of fuzzy control systems is developed. Finally, we illustrate the effectiveness of the proposed design method through an example.