Description of stability for linear time-invariant systems based on the first curvature

Wang, Y; Sun, H; Huang, S; Song, Y

Description of stability for linear time-invariant systems based on the first curvature

Wang, Y Sun, H Huang, S

Song, Y

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Publication Type:: Journal Article
Citation:: Mathematical Methods in the Applied Sciences, 2020, 43 (2), pp. 486 - 511
Issue Date:: 2020-01-30

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Field	Value	Language
dc.contributor.author	Wang, Y	en_US
dc.contributor.author	Sun, H	en_US
dc.contributor.author	Huang, S https://orcid.org/0000-0002-6124-4178	en_US
dc.contributor.author	Song, Y	en_US
dc.date.available	2020-11-14T18:03:27Z
dc.date.issued	2020-01-30	en_US
dc.identifier.citation	Mathematical Methods in the Applied Sciences, 2020, 43 (2), pp. 486 - 511	en_US
dc.identifier.issn	0170-4214	en_US
dc.identifier.uri	http://hdl.handle.net/10453/138361
dc.description.abstract	© 2019 John Wiley & Sons, Ltd. This paper focuses on using the first curvature κ(t) of trajectory to describe the stability of linear time-invariant system. We extend the results for two and three-dimensional systems (Wang, Sun, Song et al, arXiv:1808.00290) to n-dimensional systems. We prove that for a system (Formula presented.), (a) if there exists a measurable set whose Lebesgue measure is greater than zero, such that (Formula presented.) or (Formula presented.) does not exist for any initial value in this set, then the zero solution of the system is stable; (b) if the matrix A is invertible, and there exists a measurable set whose Lebesgue measure is greater than zero, such that (Formula presented.) for any initial value in this set, then the zero solution of the system is asymptotically stable.	en_US
dc.relation.ispartof	Mathematical Methods in the Applied Sciences	en_US
dc.relation.isbasedon	10.1002/mma.5896	en_US
dc.rights	info:eu-repo/semantics/openAccess
dc.subject.classification	Applied Mathematics	en_US
dc.title	Description of stability for linear time-invariant systems based on the first curvature	en_US
dc.type	Journal Article
utslib.citation.volume	2	en_US
utslib.citation.volume	43	en_US
utslib.for	0102 Applied Mathematics	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/Faculty of Engineering and Information Technology/School of Mechanical and Mechatronic Engineering
pubs.organisational-group	/University of Technology Sydney/Strength - CAS - Centre for Autonomous Systems
utslib.copyright.status	open_access	*
pubs.issue	2	en_US
pubs.publication-status	Published	en_US
pubs.volume	43	en_US

Abstract:

© 2019 John Wiley & Sons, Ltd. This paper focuses on using the first curvature κ(t) of trajectory to describe the stability of linear time-invariant system. We extend the results for two and three-dimensional systems (Wang, Sun, Song et al, arXiv:1808.00290) to n-dimensional systems. We prove that for a system (Formula presented.), (a) if there exists a measurable set whose Lebesgue measure is greater than zero, such that (Formula presented.) or (Formula presented.) does not exist for any initial value in this set, then the zero solution of the system is stable; (b) if the matrix A is invertible, and there exists a measurable set whose Lebesgue measure is greater than zero, such that (Formula presented.) for any initial value in this set, then the zero solution of the system is asymptotically stable.

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http://hdl.handle.net/10453/138361