Boundary stabilisation via event-triggered output-feedback for a class of 2 × 2 hyperbolic systems

Xia Li, Yungang Liu, Fengzhong Li and Jian Li

International Journal of Systems Science, 2020, vol. 51, issue 15, 2807-2819

Abstract: This paper is devoted to the boundary stabilisation via event-triggered output-feedback for a class of $2\times 2 $2×2 hyperbolic systems. Different from the closely related works, the system parameters are spatially varying and only one boundary measurement is available for feedback, which brings essential difficulties to the analysis and synthesis of event-triggered control. To solve the problem, by using the time-varying strategy and the infinite-dimensional backstepping technique, a novel event-triggered output-feedback controller is designed for the systems. Particularly, a time-varying event-triggering mechanism, with an extra decaying signal introduced into the threshold, is determined. It is rigorously shown that the designed event-triggered controller can guarantee that all the states of the resulting closed-loop system exponentially converge to zero in the sense of $L^2 $L2 norm while no Zeno phenomenon occurs. Two simulation examples are given to illustrate the effectiveness of the established boundary control strategy.

Date: 2020
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DOI: 10.1080/00207721.2020.1802624

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