Internal and Boundary Control of Piezoelectric Beams with Magnetic Effects and Voltage Controller: Exponential and Polynomial Decay Rates

This paper investigates a one-dimensional piezoelectric beam model that incorporates magnetic effects, significantly influencing the stability of the control system. We demonstrate that the system achieves exponential and polynomial stability using an entirely single electrical feedback (voltage control) alongside a single localized nonlinear damping mechanism of variable exponent type applied to the displacement. Various cases are discussed, and we prove that the stability outcomes depend on these variable exponents’ values. The proof method primarily employs the multiplier technique, alongside inequalities and embedding properties. Our findings provide a new contribution to the theoretical understanding of the asymptotic behavior in nonlinear models of piezoelectric beams affected by magnetic effects.