The PDP feedback control design and exponential stability for a star-shaped network of open channels

Dongxia Zhao; Yuting Pang; Yaping Guo; Junmin Wang

doi:10.1177/16878132231156056

The PDP feedback control design and exponential stability for a star-shaped network of open channels

Dongxia Zhao^*, Yuting Pang, Yaping Guo, Junmin Wang

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

This paper investigates the stability of a star-shaped network of open channels under the position and delayed position (PDP) feedback controller. Firstly, we deal with the special case of a single channel, and the well-posedness and exponential stability of the closed-loop system are established by using the semi-group theory and a strict Lyapunov function. The explicit dissipative conditions for system parameters and time-delay are presented. Then, we analyze the delay-independent stability of the closed-loop system by the method of characteristic. Next, we extend the PDP control design to the star-shaped network of (Formula presented.) channels with (Formula presented.) inlet channels and one outlet channel, and the exponential stability can be obtained similarly. Finally, we give some numerical simulations for the special case of three channels.

Original language	English
Journal	Advances in Mechanical Engineering
Volume	15
Issue number	2
DOIs	https://doi.org/10.1177/16878132231156056
Publication status	Published - Feb 2023

Keywords

Hyperbolic systems of conservation laws
Lyapunov exponential stability
PDP control design
delay-independent stability

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title = "The PDP feedback control design and exponential stability for a star-shaped network of open channels",

abstract = "This paper investigates the stability of a star-shaped network of open channels under the position and delayed position (PDP) feedback controller. Firstly, we deal with the special case of a single channel, and the well-posedness and exponential stability of the closed-loop system are established by using the semi-group theory and a strict Lyapunov function. The explicit dissipative conditions for system parameters and time-delay are presented. Then, we analyze the delay-independent stability of the closed-loop system by the method of characteristic. Next, we extend the PDP control design to the star-shaped network of (Formula presented.) channels with (Formula presented.) inlet channels and one outlet channel, and the exponential stability can be obtained similarly. Finally, we give some numerical simulations for the special case of three channels.",

keywords = "Hyperbolic systems of conservation laws, Lyapunov exponential stability, PDP control design, delay-independent stability",

author = "Dongxia Zhao and Yuting Pang and Yaping Guo and Junmin Wang",

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TY - JOUR

T1 - The PDP feedback control design and exponential stability for a star-shaped network of open channels

AU - Zhao, Dongxia

AU - Pang, Yuting

AU - Guo, Yaping

AU - Wang, Junmin

N1 - Publisher Copyright: © The Author(s) 2023.

PY - 2023/2

Y1 - 2023/2

N2 - This paper investigates the stability of a star-shaped network of open channels under the position and delayed position (PDP) feedback controller. Firstly, we deal with the special case of a single channel, and the well-posedness and exponential stability of the closed-loop system are established by using the semi-group theory and a strict Lyapunov function. The explicit dissipative conditions for system parameters and time-delay are presented. Then, we analyze the delay-independent stability of the closed-loop system by the method of characteristic. Next, we extend the PDP control design to the star-shaped network of (Formula presented.) channels with (Formula presented.) inlet channels and one outlet channel, and the exponential stability can be obtained similarly. Finally, we give some numerical simulations for the special case of three channels.

AB - This paper investigates the stability of a star-shaped network of open channels under the position and delayed position (PDP) feedback controller. Firstly, we deal with the special case of a single channel, and the well-posedness and exponential stability of the closed-loop system are established by using the semi-group theory and a strict Lyapunov function. The explicit dissipative conditions for system parameters and time-delay are presented. Then, we analyze the delay-independent stability of the closed-loop system by the method of characteristic. Next, we extend the PDP control design to the star-shaped network of (Formula presented.) channels with (Formula presented.) inlet channels and one outlet channel, and the exponential stability can be obtained similarly. Finally, we give some numerical simulations for the special case of three channels.

KW - Hyperbolic systems of conservation laws

KW - Lyapunov exponential stability

KW - PDP control design

KW - delay-independent stability

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U2 - 10.1177/16878132231156056

DO - 10.1177/16878132231156056

M3 - Article

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SN - 1687-8132

VL - 15

JO - Advances in Mechanical Engineering

JF - Advances in Mechanical Engineering

IS - 2

ER -

The PDP feedback control design and exponential stability for a star-shaped network of open channels

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