Lyapunov functions for nabla discrete fractional order systems

Wei, Y; Chen, Y; Liu, T; Wang, Y

Lyapunov functions for nabla discrete fractional order systems

Wei, Y Chen, Y Liu, T

Wang, Y

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Publication Type:: Journal Article
Citation:: ISA Transactions, 2019, 88 pp. 82 - 90
Issue Date:: 2019-05-01

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Field	Value	Language
dc.contributor.author	Wei, Y	en_US
dc.contributor.author	Chen, Y	en_US
dc.contributor.author	Liu, T https://orcid.org/0000-0001-8107-8587	en_US
dc.contributor.author	Wang, Y	en_US
dc.date.accessioned	2020-04-19T21:59:58Z
dc.date.available	2018-12-09	en_US
dc.date.available	2020-04-19T21:59:58Z
dc.date.issued	2019-05-01	en_US
dc.identifier.citation	ISA Transactions, 2019, 88 pp. 82 - 90	en_US
dc.identifier.issn	0019-0578	en_US
dc.identifier.uri	http://hdl.handle.net/10453/140098
dc.description.abstract	© 2018 ISA This paper focuses on the fractional difference of Lyapunov functions related to Riemann–Liouville, Caputo and Grünwald–Letnikov definitions. A new way of building Lyapunov functions is introduced and then five inequalities are derived for each definition. With the help of the developed inequalities, the sufficient conditions can be obtained to guarantee the asymptotic stability of the nabla discrete fractional order nonlinear systems. Finally, three illustrative examples are presented to demonstrate the validity and feasibility of the proposed theoretical results.	en_US
dc.relation.ispartof	ISA Transactions	en_US
dc.relation.isbasedon	10.1016/j.isatra.2018.12.016	en_US
dc.subject.classification	Industrial Engineering & Automation	en_US
dc.title	Lyapunov functions for nabla discrete fractional order systems	en_US
dc.type	Journal Article
utslib.citation.volume	88	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0906 Electrical and Electronic Engineering	en_US
utslib.for	0910 Manufacturing Engineering	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Students
utslib.copyright.status	closed_access
pubs.publication-status	Published	en_US
pubs.volume	88	en_US

Abstract:

© 2018 ISA This paper focuses on the fractional difference of Lyapunov functions related to Riemann–Liouville, Caputo and Grünwald–Letnikov definitions. A new way of building Lyapunov functions is introduced and then five inequalities are derived for each definition. With the help of the developed inequalities, the sufficient conditions can be obtained to guarantee the asymptotic stability of the nabla discrete fractional order nonlinear systems. Finally, three illustrative examples are presented to demonstrate the validity and feasibility of the proposed theoretical results.

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http://hdl.handle.net/10453/140098