Output feedback stabilization of Euler–Bernoulli beam equation with general corrupted boundary observation

Abstract

This paper aims to study the stabilization problem for a Euler–Bernoulli beam equation with boundary observation subject to a general external disturbance. A new infinite dimensional estimator is designed to estimate the disturbance in the corrupted boundary angular velocity signal in real time. Furthermore, a boundary output feedback control is constructed to stabilize the related system. By using the Riesz basis approach, it is proven that, in case the initial conditions satisfy certain smoothness, the closed-loop system is exponentially stable and all internal signals are bounded. Finally, a numerical example is given to show the validity of our theoretical results.

Keywords:

• Exponential stabilization
• Euler–Bernoulli beam
• general corrupted boundary observation
• disturbance rejection

2020 Mathematics Subject Classifications:

• 93D15
• 93B52
• 93C20
• 93C25

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the Natural Science Foundation of Shanghai [grant no. 19ZR1400500].