Event-Triggered Fuzzy Control of Repeated Scalar Nonlinear Systems and its Application to Chua's Circuit System

• Published in: IEEE transactions on circuits and systems. I, Regular papers Vol. 67; no. 12; pp. 5347 - 5357
• Main Authors: Wen, Yao, Chang, Hongbin, Su, Xiaojie, Assawinchaichote, Wudhichai
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Attenuation; Chaos theory; Chua’s circuit system; Circuits; Control systems; event-triggered technique; Feasibility; Feedback control; Fuzzy control; Fuzzy systems; H∞ fuzzy control; Integrated circuit modeling; Linear matrix inequalities; Mathematical analysis; Matrix converters; Nonlinear control; Nonlinear systems; repeated scalar nonlinearities
• ISSN: 1549-8328; 1558-0806
• DOI: 10.1109/TCSI.2020.2998470

This paper addresses the problem of event-triggered <inline-formula> <tex-math notation="LaTeX">\mathcal {H}_{\infty } </tex-math></inline-formula> control for continuous Takagi-Sugeno fuzzy systems with repeated scalar nonlinearities. A feasible stability solution is first proposed based on the fuzzy-rule-dependent Lyapunov functional methods and positive definite diagonally dominant matrix techniques, which not only reduces the conservativeness of the resulting closed-loop dynamic system, but also ensures the concerned fuzzy system is asymptotically stable with a specified <inline-formula> <tex-math notation="LaTeX">\mathcal {H}_{\infty } </tex-math></inline-formula> disturbance attenuation performance. Then, sufficient conditions are presented for the existence of admissible state-feedback controller, and the cone complementarity linearization approach is employed to convert the non-convex feasibility problem into a sequential minimization one subject to linear matrix inequalities, which can be validly solved by employing standard numerical software. In the end, a numerical example and a Chua's chaotic circuit system are provided to show the applicability of the proposed theories.