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Article: Robust stability of time-varying polytopic systems via parameter-dependent homogeneous Lyapunov functions
Title | Robust stability of time-varying polytopic systems via parameter-dependent homogeneous Lyapunov functions |
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Authors | |
Keywords | Bounded variation rate uncertainty LMI Lyapunov function Polytopic system Robust stability |
Issue Date | 2007 |
Publisher | Pergamon. The Journal's web site is located at http://www.elsevier.com/locate/automatica |
Citation | Automatica, 2007, v. 43 n. 2, p. 309-316 How to Cite? |
Abstract | This paper deals with robust stability analysis of linear state space systems affected by time-varying uncertainties with bounded variation rate. A new class of parameter-dependent Lyapunov functions is introduced, whose main feature is that the dependence on the uncertain parameters and the state variables are both expressed as polynomial homogeneous forms. This class of Lyapunov functions generalizes those successfully employed in the special cases of unbounded variation rates and time-invariant perturbations. The main result of the paper is a sufficient condition to determine the sought Lyapunov function, which amounts to solving an LMI feasibility problem, derived via a suitable parameterization of polynomial homogeneous forms. Moreover, lower bounds on the maximum variation rate for which robust stability of the system is preserved, are shown to be computable in terms of generalized eigenvalue problems. Numerical examples are provided to illustrate how the proposed approach compares with other techniques available in the literature. © 2006 Elsevier Ltd. All rights reserved. |
Persistent Identifier | http://hdl.handle.net/10722/73913 |
ISSN | 2023 Impact Factor: 4.8 2023 SCImago Journal Rankings: 3.502 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
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dc.contributor.author | Chesi, G | en_HK |
dc.contributor.author | Garulli, A | en_HK |
dc.contributor.author | Tesi, A | en_HK |
dc.contributor.author | Vicino, A | en_HK |
dc.date.accessioned | 2010-09-06T06:55:58Z | - |
dc.date.available | 2010-09-06T06:55:58Z | - |
dc.date.issued | 2007 | en_HK |
dc.identifier.citation | Automatica, 2007, v. 43 n. 2, p. 309-316 | en_HK |
dc.identifier.issn | 0005-1098 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/73913 | - |
dc.description.abstract | This paper deals with robust stability analysis of linear state space systems affected by time-varying uncertainties with bounded variation rate. A new class of parameter-dependent Lyapunov functions is introduced, whose main feature is that the dependence on the uncertain parameters and the state variables are both expressed as polynomial homogeneous forms. This class of Lyapunov functions generalizes those successfully employed in the special cases of unbounded variation rates and time-invariant perturbations. The main result of the paper is a sufficient condition to determine the sought Lyapunov function, which amounts to solving an LMI feasibility problem, derived via a suitable parameterization of polynomial homogeneous forms. Moreover, lower bounds on the maximum variation rate for which robust stability of the system is preserved, are shown to be computable in terms of generalized eigenvalue problems. Numerical examples are provided to illustrate how the proposed approach compares with other techniques available in the literature. © 2006 Elsevier Ltd. All rights reserved. | en_HK |
dc.language | eng | en_HK |
dc.publisher | Pergamon. The Journal's web site is located at http://www.elsevier.com/locate/automatica | en_HK |
dc.relation.ispartof | Automatica | en_HK |
dc.subject | Bounded variation rate uncertainty | en_HK |
dc.subject | LMI | en_HK |
dc.subject | Lyapunov function | en_HK |
dc.subject | Polytopic system | en_HK |
dc.subject | Robust stability | en_HK |
dc.title | Robust stability of time-varying polytopic systems via parameter-dependent homogeneous Lyapunov functions | en_HK |
dc.type | Article | en_HK |
dc.identifier.openurl | http://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0005-1098&volume=43&spage=309&epage=316&date=2007&atitle=Robust+stability+of+time-varying+polytopic+systems+via+parameter-dependent+homogeneous+Lyapunov+functions | en_HK |
dc.identifier.email | Chesi, G:chesi@eee.hku.hk | en_HK |
dc.identifier.authority | Chesi, G=rp00100 | en_HK |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.automatica.2006.08.024 | en_HK |
dc.identifier.scopus | eid_2-s2.0-33845934993 | en_HK |
dc.identifier.hkuros | 130703 | en_HK |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-33845934993&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 43 | en_HK |
dc.identifier.issue | 2 | en_HK |
dc.identifier.spage | 309 | en_HK |
dc.identifier.epage | 316 | en_HK |
dc.identifier.isi | WOS:000243670600011 | - |
dc.publisher.place | United Kingdom | en_HK |
dc.identifier.scopusauthorid | Chesi, G=7006328614 | en_HK |
dc.identifier.scopusauthorid | Garulli, A=7003697493 | en_HK |
dc.identifier.scopusauthorid | Tesi, A=7007124648 | en_HK |
dc.identifier.scopusauthorid | Vicino, A=7006250298 | en_HK |
dc.identifier.issnl | 0005-1098 | - |