H∞ synchronization of coupled delay partial differential systems via nonsingular transformation method

Kai Ning Wu; Chang Xi Li; Xinsheng Wang; Bor Sen Chen

doi:10.1016/j.apm.2015.03.062

H_∞ synchronization of coupled delay partial differential systems via nonsingular transformation method

Kai Ning Wu^*
, Chang Xi Li
, Xinsheng Wang
, Bor Sen Chen

^*Corresponding author for this work

Harbin Institute of Technology Weihai
School of Information Science and Engineering, Harbin Institute of Technology Weihai
National Tsing Hua University

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

6 Scopus citations

Abstract

This paper considers the H_∞ synchronization of coupled delay partial differential systems (PDSs). By using the nonsingular transformation method, the coupled systems are decoupled to simplify the complex H_∞ synchronization problem of coupled delay PDSs. The equivalence of the H_∞ synchronization for original coupled delay PDSs and the H_∞ stabilization of transformed decoupled delay PDSs is rigorously verified. Sufficient conditions are obtained to guarantee the H_∞ synchronization. These sufficient conditions also reflect the effect of spatial domain on the H_∞ synchronization. Moreover, when the external disturbances disappear, the asymptotical synchronization is studied. The relationship between the H_∞ synchronization and the asymptotical synchronization is also presented. At last, an example is given to illustrate the correctness of our results.

Original language	English
Pages (from-to)	4646-4654
Number of pages	9
Journal	Applied Mathematical Modelling
Volume	39
Issue number	16
DOIs	https://doi.org/10.1016/j.apm.2015.03.062
State	Published - 15 Aug 2015
Externally published	Yes

Keywords

Delay
H synchronization
Nonsingular transformation
Partial differential systems

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10.1016/j.apm.2015.03.062

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title = "H∞ synchronization of coupled delay partial differential systems via nonsingular transformation method",

abstract = "This paper considers the H∞ synchronization of coupled delay partial differential systems (PDSs). By using the nonsingular transformation method, the coupled systems are decoupled to simplify the complex H∞ synchronization problem of coupled delay PDSs. The equivalence of the H∞ synchronization for original coupled delay PDSs and the H∞ stabilization of transformed decoupled delay PDSs is rigorously verified. Sufficient conditions are obtained to guarantee the H∞ synchronization. These sufficient conditions also reflect the effect of spatial domain on the H∞ synchronization. Moreover, when the external disturbances disappear, the asymptotical synchronization is studied. The relationship between the H∞ synchronization and the asymptotical synchronization is also presented. At last, an example is given to illustrate the correctness of our results.",

keywords = "Delay, H synchronization, Nonsingular transformation, Partial differential systems",

author = "Wu, \{Kai Ning\} and Li, \{Chang Xi\} and Xinsheng Wang and Chen, \{Bor Sen\}",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2015",

month = aug,

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doi = "10.1016/j.apm.2015.03.062",

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TY - JOUR

T1 - H∞ synchronization of coupled delay partial differential systems via nonsingular transformation method

AU - Wu, Kai Ning

AU - Li, Chang Xi

AU - Wang, Xinsheng

AU - Chen, Bor Sen

PY - 2015/8/15

Y1 - 2015/8/15

N2 - This paper considers the H∞ synchronization of coupled delay partial differential systems (PDSs). By using the nonsingular transformation method, the coupled systems are decoupled to simplify the complex H∞ synchronization problem of coupled delay PDSs. The equivalence of the H∞ synchronization for original coupled delay PDSs and the H∞ stabilization of transformed decoupled delay PDSs is rigorously verified. Sufficient conditions are obtained to guarantee the H∞ synchronization. These sufficient conditions also reflect the effect of spatial domain on the H∞ synchronization. Moreover, when the external disturbances disappear, the asymptotical synchronization is studied. The relationship between the H∞ synchronization and the asymptotical synchronization is also presented. At last, an example is given to illustrate the correctness of our results.

AB - This paper considers the H∞ synchronization of coupled delay partial differential systems (PDSs). By using the nonsingular transformation method, the coupled systems are decoupled to simplify the complex H∞ synchronization problem of coupled delay PDSs. The equivalence of the H∞ synchronization for original coupled delay PDSs and the H∞ stabilization of transformed decoupled delay PDSs is rigorously verified. Sufficient conditions are obtained to guarantee the H∞ synchronization. These sufficient conditions also reflect the effect of spatial domain on the H∞ synchronization. Moreover, when the external disturbances disappear, the asymptotical synchronization is studied. The relationship between the H∞ synchronization and the asymptotical synchronization is also presented. At last, an example is given to illustrate the correctness of our results.

KW - Delay

KW - H synchronization

KW - Nonsingular transformation

KW - Partial differential systems

UR - https://www.scopus.com/pages/publications/84930752073

U2 - 10.1016/j.apm.2015.03.062

DO - 10.1016/j.apm.2015.03.062

M3 - 文章

AN - SCOPUS:84930752073

SN - 0307-904X

VL - 39

SP - 4646

EP - 4654

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

IS - 16

ER -

H_∞ synchronization of coupled delay partial differential systems via nonsingular transformation method

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