H PID Control for Discrete-Time Fuzzy Systems With Infinite-Distributed Delays Under Round-Robin Communication Protocol

• Published in: IEEE transactions on fuzzy systems Vol. 30; no. 6; pp. 1875 - 1888
• Main Authors: Wang, Yezheng, Wang, Zidong, Zou, Lei, Dong, Hongli
• Format: Journal Article
• Language: English
• Published: IEEE 01.06.2022
• Subjects: Communication networks; Cone complementarity linearization; Control systems; fuzzy systems; linear matrix inequality (LMI); Optimization; PD control; PI control; proportional–integral–derivative (PID) control; Protocols; round-robin (RR) protocol; Symmetric matrices
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2021.3069329

This article is concerned with the <inline-formula><tex-math notation="LaTeX">H_{\infty }</tex-math></inline-formula> proportional-integral-derivative (PID) control problem for class of discrete-time Takagi-Sugeno fuzzy systems subject to infinite-distributed time delays and round-robin (RR) protocol scheduling effects. The information exchange between the sensors and the controller is conducted through a shared communication network. For the purpose of alleviating possible data collision, the well-known RR communication protocol is deployed to schedule the data transmissions. To stabilize the target system with guaranteed <inline-formula><tex-math notation="LaTeX">H_{\infty }</tex-math></inline-formula> performance index, a novel yet easy-to-implement fuzzy PID controller is developed whose integral term is calculated based on the past measurements defined in a limited time window with hope to improve computational efficiency and reduce accumulation error. Based on the Lyapunov stability theory and the convex optimization technique, sufficient conditions are derived to ensure the exponential stability as well as the <inline-formula><tex-math notation="LaTeX">H_{\infty }</tex-math></inline-formula> disturbance attenuation/rejection capacity of the underlying system. Furthermore, by utilizing the cone complementarity linearization algorithm, the nonconvex controller design problem is transformed into an iterative optimization one that facilitates the controller implementation. Finally, simulation examples are given to show the effectiveness and correctness of the developed control method.