Global finite-time stability of delayed quaternion-valued neural networks based on a class of extended Lyapunov–Razumikhin methods

Chengsheng Li; Jinde Cao; Ardak Kashkynbayev

doi:10.1007/s11571-022-09860-9

Global finite-time stability of delayed quaternion-valued neural networks based on a class of extended Lyapunov–Razumikhin methods

Chengsheng Li, Jinde Cao, Ardak Kashkynbayev

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

2 Citations (Scopus)

Abstract

In this paper, a class of global finite-time stability problem for quaternion-valued neural networks with time-varying delays are investigated by adopting an extended modification Lyapunov–Razumikhin (L–R) method and a new upper bounds estimation of system solution in terms of convergence rate was obtained. Firstly, a new extended method of L–R is proposed to solve the general difficulty to find a proper Lyapunov functional. Then, a new suitable controller is designed, the new conditions of inequalities global finite-time stability are obtained via combining with the former proposed L–R method in the separated real-valued system. Finally, for purpose of verifying the availability of the theorem presented, two given illustrative examples are shown.

Original language	English
Pages (from-to)	729 - 739
Number of pages	11
Journal	Cognitive Neurodynamics
Volume	17
Issue number	3
DOIs	https://doi.org/10.1007/s11571-022-09860-9
Publication status	Published - Jun 2023

Keywords

Global finite-time
Modified L–R method
Quaternion
Stability
Time varying delays

ASJC Scopus subject areas

Cognitive Neuroscience

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10.1007/s11571-022-09860-9

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title = "Global finite-time stability of delayed quaternion-valued neural networks based on a class of extended Lyapunov–Razumikhin methods",

abstract = "In this paper, a class of global finite-time stability problem for quaternion-valued neural networks with time-varying delays are investigated by adopting an extended modification Lyapunov–Razumikhin (L–R) method and a new upper bounds estimation of system solution in terms of convergence rate was obtained. Firstly, a new extended method of L–R is proposed to solve the general difficulty to find a proper Lyapunov functional. Then, a new suitable controller is designed, the new conditions of inequalities global finite-time stability are obtained via combining with the former proposed L–R method in the separated real-valued system. Finally, for purpose of verifying the availability of the theorem presented, two given illustrative examples are shown.",

keywords = "Global finite-time, Modified L–R method, Quaternion, Stability, Time varying delays",

author = "Chengsheng Li and Jinde Cao and Ardak Kashkynbayev",

note = "Funding Information: This work was supported by the National Nature Science Foundation of China under Grant Nos. 61833005. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature B.V.",

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AU - Li, Chengsheng

AU - Cao, Jinde

AU - Kashkynbayev, Ardak

N1 - Funding Information: This work was supported by the National Nature Science Foundation of China under Grant Nos. 61833005. Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Nature B.V.

PY - 2023/6

Y1 - 2023/6

N2 - In this paper, a class of global finite-time stability problem for quaternion-valued neural networks with time-varying delays are investigated by adopting an extended modification Lyapunov–Razumikhin (L–R) method and a new upper bounds estimation of system solution in terms of convergence rate was obtained. Firstly, a new extended method of L–R is proposed to solve the general difficulty to find a proper Lyapunov functional. Then, a new suitable controller is designed, the new conditions of inequalities global finite-time stability are obtained via combining with the former proposed L–R method in the separated real-valued system. Finally, for purpose of verifying the availability of the theorem presented, two given illustrative examples are shown.

AB - In this paper, a class of global finite-time stability problem for quaternion-valued neural networks with time-varying delays are investigated by adopting an extended modification Lyapunov–Razumikhin (L–R) method and a new upper bounds estimation of system solution in terms of convergence rate was obtained. Firstly, a new extended method of L–R is proposed to solve the general difficulty to find a proper Lyapunov functional. Then, a new suitable controller is designed, the new conditions of inequalities global finite-time stability are obtained via combining with the former proposed L–R method in the separated real-valued system. Finally, for purpose of verifying the availability of the theorem presented, two given illustrative examples are shown.

KW - Global finite-time

KW - Modified L–R method

KW - Quaternion

KW - Stability

KW - Time varying delays

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Global finite-time stability of delayed quaternion-valued neural networks based on a class of extended Lyapunov–Razumikhin methods

Abstract

Keywords

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