File Download
  Links for fulltext
     (May Require Subscription)
Supplementary

Article: Establishing robust stability of discrete-time systems with time-varying uncertainty: the Gram-SOS Approach

TitleEstablishing robust stability of discrete-time systems with time-varying uncertainty: the Gram-SOS Approach
Authors
Issue Date2014
PublisherElsevier. The Journal's web site is located at http://www.elsevier.com/locate/automatica
Citation
Automatica, 2014, v. 50 n. 11, p. 2813-2821 How to Cite?
AbstractThis paper addresses the problem of establishing robust asymptotical stability of discrete-time linear systems polynomially affected by time-varying uncertainty confined into a polytope. A linear matrix inequality (LMI) condition for establishing robust asymptotical stability is proposed by introducing a novel approach for establishing the existence of a common homogeneous polynomial Lyapunov function (HPLF). This approach consists, firstly, of introducing a Gram matrix built with respect to the state and parametrized by an arbitrary vector function of the uncertainty, and secondly, of requiring that a transformation of the introduced Gram matrix is a sum of squares (SOS) of matrix polynomials. The approach, hence, is referred to as a Gram-SOS approach. It is shown that the proposed LMI condition is sufficient for any degree of the HPLF candidate, that includes quadratic robust stability as a special case, and that is also necessary for a sufficiently large degree of the HPLF candidate. Numerical examples also show that the proposed LMI condition can outperform alternative ones in terms of conservatism and computational burden. © 2014 Elsevier Ltd.
Persistent Identifierhttp://hdl.handle.net/10722/211752
ISSN
2015 Impact Factor: 3.635
2015 SCImago Journal Rankings: 4.315

 

DC FieldValueLanguage
dc.contributor.authorChesi, G-
dc.date.accessioned2015-07-21T02:09:58Z-
dc.date.available2015-07-21T02:09:58Z-
dc.date.issued2014-
dc.identifier.citationAutomatica, 2014, v. 50 n. 11, p. 2813-2821-
dc.identifier.issn0005-1098-
dc.identifier.urihttp://hdl.handle.net/10722/211752-
dc.description.abstractThis paper addresses the problem of establishing robust asymptotical stability of discrete-time linear systems polynomially affected by time-varying uncertainty confined into a polytope. A linear matrix inequality (LMI) condition for establishing robust asymptotical stability is proposed by introducing a novel approach for establishing the existence of a common homogeneous polynomial Lyapunov function (HPLF). This approach consists, firstly, of introducing a Gram matrix built with respect to the state and parametrized by an arbitrary vector function of the uncertainty, and secondly, of requiring that a transformation of the introduced Gram matrix is a sum of squares (SOS) of matrix polynomials. The approach, hence, is referred to as a Gram-SOS approach. It is shown that the proposed LMI condition is sufficient for any degree of the HPLF candidate, that includes quadratic robust stability as a special case, and that is also necessary for a sufficiently large degree of the HPLF candidate. Numerical examples also show that the proposed LMI condition can outperform alternative ones in terms of conservatism and computational burden. © 2014 Elsevier Ltd.-
dc.languageeng-
dc.publisherElsevier. The Journal's web site is located at http://www.elsevier.com/locate/automatica-
dc.relation.ispartofAutomatica-
dc.rights© 2014. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleEstablishing robust stability of discrete-time systems with time-varying uncertainty: the Gram-SOS Approach-
dc.typeArticle-
dc.identifier.emailChesi, G: chesi@eee.hku.hk-
dc.identifier.authorityChesi, G=rp00100-
dc.description.naturepostprint-
dc.identifier.doi10.1016/j.automatica.2014.10.007-
dc.identifier.hkuros245055-
dc.identifier.volume50-
dc.identifier.issue11-
dc.identifier.spage2813-
dc.identifier.epage2821-
dc.publisher.placeUnited Kingdom-

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats