Finite-time boundedness synthesis for Bouc-Wen hysteresis dynamic systems using non-fragile event-triggered Takagi-Sugeno fuzzy control

Abstract

This paper investigates the finite-time (FT) control problem for Takagi-Sugeno (T-S) fuzzy Bouc-Wen (B-W) hysteresis systems under a fuzzy event-triggered (ET) non-fragile control framework. A novel T-S fuzzy hysteresis state estimator is developed to estimate the virtual hysteresis state, enabling accurate compensation of hysteresis effects in networked control environments. To reduce communication burden while preserving closed-loop performance, a fuzzy ET mechanism is incorporated into the control architecture, allowing adaptive transmission based on system dynamics. In contrast to existing hysteresis control methods, the proposed scheme integrates a newly developed T-S fuzzy hysteresis model, an ET mechanism, and a non-fragile control design within a unified FT framework. The main objective is to guarantee FT boundedness (FTB) of the closed-loop T-S fuzzy B-W hysteresis system while simultaneously achieving prescribed FT mixed H_∞ and passivity performance indices. By employing the Lyapunov-Krasovskii functional methodology, a set of novel sufficient conditions is derived in terms of linear matrix inequalities, ensuring FTB and the desired performance criteria. The effectiveness and feasibility of the proposed control strategy are validated through three numerical examples.

Keywords

Bouc-Wen hysteresis behavior / Event-triggered mechanism / Finite-time boundedness / Non-fragile controller / Fuzzy system

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