Geometric homogeneity with applications to finite-time stability
dc.contributor.author | Bernstein, Dennis S. | en_US |
dc.contributor.author | Bhat, Sanjay P. | en_US |
dc.date.accessioned | 2006-09-11T17:09:09Z | |
dc.date.available | 2006-09-11T17:09:09Z | |
dc.date.issued | 2005-06 | en_US |
dc.identifier.citation | Bhat, S. P.; Bernstein, D. S.; (2005). "Geometric homogeneity with applications to finite-time stability." Mathematics of Control, Signals, and Systems 17(2): 101-127. <http://hdl.handle.net/2027.42/45918> | en_US |
dc.identifier.issn | 0932-4194 | en_US |
dc.identifier.issn | 1435-568X | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/45918 | |
dc.description.abstract | This paper studies properties of homogeneous systems in a geometric, coordinate-free setting. A key contribution of this paper is a result relating regularity properties of a homogeneous function to its degree of homogeneity and the local behavior of the dilation near the origin. This result makes it possible to extend previous results on homogeneous systems to the geometric framework. As an application of our results, we consider finite-time stability of homogeneous systems. The main result that links homogeneity and finite-time stability is that a homogeneous system is finite-time stable if and only if it is asymptotically stable and has a negative degree of homogeneity. We also show that the assumption of homogeneity leads to stronger properties for finite-time stable systems. | en_US |
dc.format.extent | 276900 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Springer-Verlag; Springer-Verlag London Limited | en_US |
dc.subject.other | Lyapunov Theory | en_US |
dc.subject.other | Mathematics | en_US |
dc.subject.other | Stability | en_US |
dc.subject.other | Geometric Homogeneity | en_US |
dc.subject.other | Communications Engineering, Networks | en_US |
dc.subject.other | Mathematics, General | en_US |
dc.subject.other | Control Engineering | en_US |
dc.subject.other | Homogeneous Systems | en_US |
dc.subject.other | Finite-time Stability | en_US |
dc.title | Geometric homogeneity with applications to finite-time stability | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Aerospace Engineering, , The University of Michigan, , Ann Arbor, MI, 48109-2140, USA | en_US |
dc.contributor.affiliationother | Department of Aerospace Engineering, , Indian Institute of Technology, , Powai, Mumbai, 400076, India | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/45918/1/498_2005_Article_151.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/s00498-005-0151-x | en_US |
dc.identifier.source | Mathematics of Control, Signals, and Systems | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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