Exponential stabilization for magnetic effected piezoelectric beams with time-varying delay and time-dependent weights

TL;DR

This paper studies the exponential stabilization of magnetic-effect piezoelectric beams with interior time-varying delays and weights, using Lyapunov functionals and semigroup theory to prove stability.

Contribution

It introduces a novel approach combining Lyapunov functionals and semigroup theory to handle delays and weights in piezoelectric beam stabilization.

Findings

Established existence and uniqueness of solutions.

Proved exponential stability under certain conditions.

Developed a new Lyapunov functional for delayed systems.

Abstract

This paper is concerned with system of magnetic effected piezoelectric beams with interior time-varying delay and time-dependent weights, in which the beam is clamped at the two side points subject to a single distributed state feedback controller with a time-varying delay. By combining the semigroup theory with Kato's variable norm technique, we obtain the existence and uniqueness of solution. By imposing appropriate assumptions on the time-varying delay term and time-dependent weights, we introduce suitable perturbed Lyapunov functional to obtain exponential stability estimates.