A new approach for stabilization of Heat-ODE cascaded systems with boundary delayed control-Reference-Cited by-同舟云学术

A new approach for stabilization of Heat-ODE cascaded systems with boundary delayed control

Published:2021-12-17 Issue: Volume: Page:
ISSN:0265-0754
Container-title:IMA Journal of Mathematical Control and Information
language:en
Short-container-title:

Author:

Zhang Li¹,Xu Gen Qi²,Mastorakis Nikos E³

Affiliation:

1. School of Science, Tianjin University of Commerce, Tianjin 300134, P. R. China and School of Mathematics, Tianjin University, Tianjin 300350, P. R. China

2. School of Mathematics, Tianjin University, Tianjin 300350, P. R. China

3. Department of Industrial Engineering, Technical University of Sofia, Sofia 1000, Bulgaria

Abstract

Abstract The uniform stabilization problem is addressed for a Heat-ODE cascaded system with boundary delayed control. A simple, direct and easily calculated controller is proposed, in which the known control law is sufficiently applied. With the controller the cascaded system with delayed control is exponentially stabilized. In particular, in the proof of stability, a resolvent for a more complicated integral equation is given. As an application, an equivalent transformation between the closed loop system and a stable system is constructed. The effectiveness of the control-predictor is shown by simulation in the presence of control delay.

Funder

National Natural Science Foundation of China

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Control and Optimization,Control and Systems Engineering

Link

https://academic.oup.com/imamci/advance-article-pdf/doi/10.1093/imamci/dnab037/41794986/dnab037.pdf

Reference45 articles.

1. Delayed-positive feedback can stabilize oscillatory systems;Abdallah,1993

2. Observer design for a class of nonlinear ODE-PDE cascade systems;Ahmed-Ali;Syst. Control Lett.,2015

3. Feedback stabilization of a class of evolution equations with delay;Ait Benhassi;J. Evol. Equ.,2009

4. An example on the effect of time delays in boundary feedback stabilization of wave equations;Datko;SIAM J. Control Optim.,1986

5. Not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks;Datko;SIAM J. Control Optim.,1988

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Uniform stabilization of a Schrödinger equation with partial Dirichlet delayed control;IMA Journal of Mathematical Control and Information;2023-09

2. State feedback controller design of fractional ordinary differential equations coupled with a fractional reaction–advection–diffusion equation with delay;Transactions of the Institute of Measurement and Control;2023-07-11