Uniform stabilization of 1-d wave equation with anti-damping and delayed control

Zhang, Li; Xu, Guan; Chen, Hao

doi:10.1016/j.jfranklin.2020.09.034

Cited by 7 publications

(1 citation statement)

References 38 publications

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“…Many control problems with delays have been widely studied [1,5,9,7,10,12,17,16,18,28] due to the instability caused by delays. So far, there occur many methods to deal with these control problems, among which backstepping is an effective one [3,4,6,20,22,25,24,30,29]. In practical application, there is usually an error between the identified delay and the exact delay, which is called "delay mismatch".…”

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confidence: 99%

Robustness of output feedback control for a wave-ODE cascaded system to the input delay mismatch

Feng,

Zhang,

Zou

2024

EECT

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This paper investigates the robustness of output feedback control to the input delay mismatch for a wave-ODE cascaded system with the timevarying input and output delays. Firstly, we convert the output delay into a transport equation, resulting in a wave-ODE-transport coupled system. Secondly, we design an output feedback control for the coupled system without input delay mismatch, and prove the well-posedness and exponential stability of the closed-loop system. Then, the key point is that we prove that this control still works when there exists an input delay mismatch. Finally, some numerical simulations are given, which illustrate the effectiveness and robustness of the proposed control.

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mentioning

confidence: 99%

Robustness of output feedback control for a wave-ODE cascaded system to the input delay mismatch

Feng,

Zhang,

Zou

2024

EECT

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Stabilization of an Euler-Bernoulli Beam with Distributed Damping Under Time Delays in the Boundary

Chen

Xie

2022

Acta Appl Math

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

Zhang

Mastorakis

2021

IMA Journal of Mathematical Control and Information

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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.

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Uniform stabilization of 1-d wave equation with anti-damping and delayed control

Cited by 7 publications

References 38 publications

Robustness of output feedback control for a wave-ODE cascaded system to the input delay mismatch

Robustness of output feedback control for a wave-ODE cascaded system to the input delay mismatch

Stabilization of an Euler-Bernoulli Beam with Distributed Damping Under Time Delays in the Boundary

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

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