Time-Delayed and Quantized Fuzzy Systems: Stability Analysis and Controller Design

In this paper, the design methodology of digital fuzzy controller(DFC) for the systems with time-delay is presented and the qualitative effects of the quantizers in digital implementation of a fuzzy controllers are investigated. We propose the fuzzy feed-back controller whose output is delayed with unit sampling period and 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. Furthermore, we analyze the stability of the quantized fuzzy system. Our results prove that when quantization os taken into account, one only has convergence to some small neighborhood about origin. We develop a fuzzy control system for backing up a computer-simulated truck-trailer with the consideration of time-delay and quantization effect. By using the proposed method, we analyze the quantization effect to the system and design a DFC which guarantees the stability of the control system in the presence of time-delay.