Stability and robust stabilization of discrete-time switched systems with time-delays: LMI approach
We present sufficient linear matrix inequality conditions for asymptotic stability and stabilizability of switched discrete-time linear systems subject to time-delays and norm bounded uncertainties. Namely, if these LMIs are solvable then, the switched system is exponentially stable for arbitrary sw...
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| Published in | Applied mathematics and computation Vol. 206; no. 2; pp. 570 - 578 |
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| Main Author | |
| Format | Journal Article Conference Proceeding |
| Language | English |
| Published |
Amsterdam
Elsevier Inc
15.12.2008
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0096-3003 1873-5649 |
| DOI | 10.1016/j.amc.2008.05.149 |
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| Abstract | We present sufficient linear matrix inequality conditions for asymptotic stability and stabilizability of switched discrete-time linear systems subject to time-delays and norm bounded uncertainties. Namely, if these LMIs are solvable then, the switched system is exponentially stable for arbitrary switching. In fact, we show that any family of switched time-delay systems satisfying these conditions possesses a quadratic common Lyapunov function. We also discuss the implication of this result on the stabilizability of this class of systems by switching controllers that use common Lyapunov functions. We show that even the analysis is carried out through a common Lyapunov function, the applied controller is mode dependent. |
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| AbstractList | We present sufficient linear matrix inequality conditions for asymptotic stability and stabilizability of switched discrete-time linear systems subject to time-delays and norm bounded uncertainties. Namely, if these LMIs are solvable then, the switched system is exponentially stable for arbitrary switching. In fact, we show that any family of switched time-delay systems satisfying these conditions possesses a quadratic common Lyapunov function. We also discuss the implication of this result on the stabilizability of this class of systems by switching controllers that use common Lyapunov functions. We show that even the analysis is carried out through a common Lyapunov function, the applied controller is mode dependent. |
| Author | Ibrir, Salim |
| Author_xml | – sequence: 1 givenname: Salim surname: Ibrir fullname: Ibrir, Salim email: sibrir@encs.concordia.ca organization: Department of Mechanical and Industrial Engineering, Concordia University, 1455 De Maisonneuve Boulvard West, Montréal, Canada H3G 1M8 |
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| CitedBy_id | crossref_primary_10_1016_j_jfranklin_2011_01_002 crossref_primary_10_4028_www_scientific_net_AMM_479_480_983 crossref_primary_10_1016_j_isatra_2016_08_010 crossref_primary_10_1016_j_jfranklin_2012_04_001 crossref_primary_10_1016_S1665_6423_14_71677_3 crossref_primary_10_1016_j_amc_2010_03_033 crossref_primary_10_1186_1687_1847_2013_39 crossref_primary_10_1186_1687_1847_2014_233 crossref_primary_10_1007_s12555_013_0351_y crossref_primary_10_1155_2013_134296 |
| Cites_doi | 10.1109/ACC.2000.878830 10.1016/0005-1098(96)00074-X 10.1016/S0167-6911(00)00113-4 10.1109/9.664149 10.1016/S0005-1098(99)00057-6 10.1016/S0005-1098(98)00054-5 10.1109/9.664150 10.1109/37.793443 10.1109/9.618244 10.1080/0020717021000023735 10.23919/ACC.1991.4791667 |
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| Keywords | Switched systems Discrete-time systems Time-delay systems Convex optimization System theory Numerical linear algebra Optimization method Linear time Discrete system Delay system Systems theory Direct method Asymptotic stability Numerical analysis Sufficient condition Linear system Matrix inversion Applied mathematics Discrete time Numerical stability Lyapunov function Mathematical programming |
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| SubjectTerms | Algebra Algebraic geometry Calculus of variations and optimal control Convex optimization Discrete-time systems Exact sciences and technology Global analysis, analysis on manifolds Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Sciences and techniques of general use Switched systems System theory Time-delay systems Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| Title | Stability and robust stabilization of discrete-time switched systems with time-delays: LMI approach |
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