Exponential input-to-state stability of delay Korteweg–de Vries–Burgers equations

Shuang Liang; Deqiong Ding; Kai Ning Wu

doi:10.1016/j.cnsns.2023.107218

Exponential input-to-state stability of delay Korteweg–de Vries–Burgers equations

Shuang Liang
, Deqiong Ding
, Kai Ning Wu^*

^*Corresponding author for this work

Harbin Institute of Technology Weihai

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

10 Scopus citations

Abstract

The exponential input-to-state stability (EISS) is studied for delay Korteweg–de Vries–Burgers (DKdVB) equations. DKdVB equations are considered with distributed input and boundary input. Making use of the Lyapunov–Krasovskii functional method and inequality techniques, a sufficient condition is established to ensure the EISS for DKdVB equations. Besides the impact of the time delay on the EISS, this sufficient condition also shows the effect of the diffusion term on the EISS. In case of uncertainties of system's coefficients, robust EISS of uncertain DKdVB equations is investigated. A criterion is obtained to guarantee the EISS for the uncertain DKdVB equation. Two numerical simulation examples are given to illustrate the validity of the derived results.

Original language	English
Article number	107218
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	121
DOIs	https://doi.org/10.1016/j.cnsns.2023.107218
State	Published - 15 Jun 2023
Externally published	Yes

Keywords

Exponential input-to-state stability
Korteweg–de Vries–Burgers equations
Robust stability
Varying delay

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10.1016/j.cnsns.2023.107218

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@article{53aa67f99d6e4de7bb58c2c92ee0e021,

title = "Exponential input-to-state stability of delay Korteweg–de Vries–Burgers equations",

abstract = "The exponential input-to-state stability (EISS) is studied for delay Korteweg–de Vries–Burgers (DKdVB) equations. DKdVB equations are considered with distributed input and boundary input. Making use of the Lyapunov–Krasovskii functional method and inequality techniques, a sufficient condition is established to ensure the EISS for DKdVB equations. Besides the impact of the time delay on the EISS, this sufficient condition also shows the effect of the diffusion term on the EISS. In case of uncertainties of system's coefficients, robust EISS of uncertain DKdVB equations is investigated. A criterion is obtained to guarantee the EISS for the uncertain DKdVB equation. Two numerical simulation examples are given to illustrate the validity of the derived results.",

keywords = "Exponential input-to-state stability, Korteweg–de Vries–Burgers equations, Robust stability, Varying delay",

author = "Shuang Liang and Deqiong Ding and Wu, \{Kai Ning\}",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier B.V.",

year = "2023",

month = jun,

day = "15",

doi = "10.1016/j.cnsns.2023.107218",

language = "英语",

volume = "121",

journal = "Communications in Nonlinear Science and Numerical Simulation",

issn = "1007-5704",

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TY - JOUR

T1 - Exponential input-to-state stability of delay Korteweg–de Vries–Burgers equations

AU - Liang, Shuang

AU - Ding, Deqiong

AU - Wu, Kai Ning

PY - 2023/6/15

Y1 - 2023/6/15

N2 - The exponential input-to-state stability (EISS) is studied for delay Korteweg–de Vries–Burgers (DKdVB) equations. DKdVB equations are considered with distributed input and boundary input. Making use of the Lyapunov–Krasovskii functional method and inequality techniques, a sufficient condition is established to ensure the EISS for DKdVB equations. Besides the impact of the time delay on the EISS, this sufficient condition also shows the effect of the diffusion term on the EISS. In case of uncertainties of system's coefficients, robust EISS of uncertain DKdVB equations is investigated. A criterion is obtained to guarantee the EISS for the uncertain DKdVB equation. Two numerical simulation examples are given to illustrate the validity of the derived results.

AB - The exponential input-to-state stability (EISS) is studied for delay Korteweg–de Vries–Burgers (DKdVB) equations. DKdVB equations are considered with distributed input and boundary input. Making use of the Lyapunov–Krasovskii functional method and inequality techniques, a sufficient condition is established to ensure the EISS for DKdVB equations. Besides the impact of the time delay on the EISS, this sufficient condition also shows the effect of the diffusion term on the EISS. In case of uncertainties of system's coefficients, robust EISS of uncertain DKdVB equations is investigated. A criterion is obtained to guarantee the EISS for the uncertain DKdVB equation. Two numerical simulation examples are given to illustrate the validity of the derived results.

KW - Exponential input-to-state stability

KW - Korteweg–de Vries–Burgers equations

KW - Robust stability

KW - Varying delay

UR - https://www.scopus.com/pages/publications/85150380717

U2 - 10.1016/j.cnsns.2023.107218

DO - 10.1016/j.cnsns.2023.107218

M3 - 文章

AN - SCOPUS:85150380717

SN - 1007-5704

VL - 121

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

M1 - 107218

ER -

Exponential input-to-state stability of delay Korteweg–de Vries–Burgers equations

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Keywords

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