Volume 29, 2023
|Number of page(s)
|08 September 2023
Uniformly exponential stability of semi-discrete scheme for a vibration cable with a tip mass under observer-based feedback control
School of Mathematics and Physics North China Electrical Power University, Beijing 102206, PR China
2 Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100190
3 School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, PR China
* Corresponding author: firstname.lastname@example.org
Accepted: 26 July 2023
In this paper, we consider uniformly exponential approximation for a vibrating cable with tip mass under a non-collocated output stabilizing feedback control. By designing an observer-based output feedback control, the closed-loop system is composed of the coupled same type of PDEs and ODEs. By order reduction method, we find a global Lyapunov functional for the closed-loop system. The closed-loop system is then semi-discretized by the finite difference method. For the discrete systems, we also construct the Lyapunov functions. The uniform exponential stability of the semi-discretized systems is then established analogously as the proof for the continuous counterpart via an indirect Lyapunov functional approach.
Mathematics Subject Classification: 35L05 / 49M25 / 34D20 / 65L20 / 65N12
Key words: Wave equation / tip mass / exponential stability / finite-difference scheme
© The authors. Published by EDP Sciences, SMAI 2023
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