File Download
Links for fulltext
(May Require Subscription)
- Publisher Website: 10.1016/j.automatica.2014.10.007
- Scopus: eid_2-s2.0-84911383151
- WOS: WOS:000345727700006
- Find via
Supplementary
- Citations:
- Appears in Collections:
Article: Establishing robust stability of discrete-time systems with time-varying uncertainty: the Gram-SOS Approach
Title | Establishing robust stability of discrete-time systems with time-varying uncertainty: the Gram-SOS Approach |
---|---|
Authors | |
Keywords | Discrete-time Robust stability Time-varying Uncertain system |
Issue Date | 2014 |
Publisher | Elsevier. 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? |
Abstract | This 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 Identifier | http://hdl.handle.net/10722/211752 |
ISSN | 2023 Impact Factor: 4.8 2023 SCImago Journal Rankings: 3.502 |
ISI Accession Number ID |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Chesi, G | - |
dc.date.accessioned | 2015-07-21T02:09:58Z | - |
dc.date.available | 2015-07-21T02:09:58Z | - |
dc.date.issued | 2014 | - |
dc.identifier.citation | Automatica, 2014, v. 50 n. 11, p. 2813-2821 | - |
dc.identifier.issn | 0005-1098 | - |
dc.identifier.uri | http://hdl.handle.net/10722/211752 | - |
dc.description.abstract | This 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.language | eng | - |
dc.publisher | Elsevier. The Journal's web site is located at http://www.elsevier.com/locate/automatica | - |
dc.relation.ispartof | Automatica | - |
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.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.subject | Discrete-time | - |
dc.subject | Robust stability | - |
dc.subject | Time-varying | - |
dc.subject | Uncertain system | - |
dc.title | Establishing robust stability of discrete-time systems with time-varying uncertainty: the Gram-SOS Approach | - |
dc.type | Article | - |
dc.identifier.email | Chesi, G: chesi@eee.hku.hk | - |
dc.identifier.authority | Chesi, G=rp00100 | - |
dc.description.nature | postprint | - |
dc.identifier.doi | 10.1016/j.automatica.2014.10.007 | - |
dc.identifier.scopus | eid_2-s2.0-84911383151 | - |
dc.identifier.hkuros | 245055 | - |
dc.identifier.volume | 50 | - |
dc.identifier.issue | 11 | - |
dc.identifier.spage | 2813 | - |
dc.identifier.epage | 2821 | - |
dc.identifier.isi | WOS:000345727700006 | - |
dc.publisher.place | United Kingdom | - |
dc.identifier.issnl | 0005-1098 | - |