On the stability of fuzzy proportional-derivative control systems

This paper presents the stability analysis of a fuzzy proportional-derivative (PD) controller. The proposed fuzzy PD controller has the same simple linear structure as the conventional PD controller in the proportional and derivative parts, but the two fuzzy control gains are nonlinear functions of the input error signals and they both have self-tuning control capability. The fuzzy PD controller has the same performance as the conventional PD controller for linear processes, yet improves the control capability for nonlinear and uncertain processes. We employ the "small gain theorem" to analyze the bounded-input/bounded-output stability of a general nonlinear fuzzy PD control system, deriving a simple and realistic sufficient condition for the stability of the system.<<ETX>>