Event-triggered damping stabilization of Euler–Bernoulli beam equation

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.