Digital stabilization of fuzzy systems with time-delay and its application to backing up control of a truck-trailer

This paper presents the design methodology of digital fuzzy controller(DFC) for the systems with time-delay. We propose the fuzzy feedback controller whose output is delayed with unit sampling period and predicted. The analysis and the design problem considering time-delay become very easy because the proposed controller is syncronized with the sampling time. The stabilization problem of the digital fuzzy system with time-delay is solved by linear matrix inequality(LMI) theory. Convex optimization techniques are utilized to solve the stable feedback gains and a common Lyapunov function for designed fuzzy control system. Furthermore, we develop a control system for backing up a computer-simulated truck-trailer with the consideration of time-delay. By using the proposed method, we design a DFC which guarantees the stability of the control system in the presence of time-delay.