Event-Triggered Fuzzy Control of Repeated Scalar Nonlinear Systems and its Application to Chua's Circuit System - Wen, Yao; Chang, Hongbin; Su, Xiaojie; Assawinchaichote, Wudhichai (IEEE transactions on circuits and systems. I, Regular papers, 2020)
This paper addresses the problem of event-triggered \mathcal {H}_{∞ } 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 \mathcal {H}_{∞ } 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.