Event-triggered damping stabilization of Euler–Bernoulli beam equation

¹ Department of Mathematics, Huzhou University, Huzhou 313000, PR China
² Université Claude Bernard Lyon 1, Department of Mechanics, LAGEPP, CNRS UMR 5007, Villeurbanne F-69622, France
³ School of Mathematics and Statistics, Central South University, Changsha 410075, PR China
⁴ Department of Mathematics, University of Georgia, Athens, GA 30602, USA
⁵ Department of Mathematics, Donghua University, Shanghai 201620, PR China

^* Corresponding author: cheng-zhong.xu@univ-lyon1.fr; hczhou@amss.ac.cn

Received: 4 September 2024
Accepted: 25 July 2025

Abstract

This article deals with the distributed event-triggered feedback stabilization for an Euler–Bernoulli beam equation. Novel event-triggered rules with distributed damping control laws are proposed to stabilize the beam system: one rule is built based on the beam energy and the other on the beam state information plus an exponentially time-decreasing term to reduce the switching frequency of actuators. Well-posedness and no Zeno behaviour are completely proven for our event-triggered sampled feedback control systems. Moreover, by developing Lyapunov functionals, sufficient LMI-type conditions on the system parameters are proposed to ensure exponential stabilization of the event-triggered feedback beam system. On the other hand, we show that the exponential stabilization is not achievable by using the periodic sampled feedback control laws (i.e., constant sample and hold) no matter what the sampling period is. Numerical simulations are presented to validate the stabilization performance of our proposed event-triggered control strategy.