Convergence Properties for Discrete-Time Nonlinear Systems
Three similar convergence notions are considered. Two of them are the long established notions of convergent dynamics and incremental stability. The other is the more recent notion of contraction analysis. All three convergence notions require that all solutions of a system converge to each other. I...
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| Veröffentlicht in: | IEEE transactions on automatic control 2019-08, Vol.64 (8), p.3415-3422 |
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| container_title | IEEE transactions on automatic control |
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| creator | Tran, Duc N. Ruffer, Bjorn S. Kellett, Christopher M. |
| description | Three similar convergence notions are considered. Two of them are the long established notions of convergent dynamics and incremental stability. The other is the more recent notion of contraction analysis. All three convergence notions require that all solutions of a system converge to each other. In this note, we investigate the differences between these convergence properties for discrete-time and time-varying nonlinear systems by comparing the properties in pairs and using examples. We also demonstrate a time-varying smooth Lyapunov function characterization for each of these convergence notions, and, with appropriate assumptions, we provide several sufficient conditions to establish relationships between these properties in terms of Lyapunov functions. |
| doi_str_mv | 10.1109/TAC.2018.2879951 |
| format | Article |
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Two of them are the long established notions of convergent dynamics and incremental stability. The other is the more recent notion of contraction analysis. All three convergence notions require that all solutions of a system converge to each other. In this note, we investigate the differences between these convergence properties for discrete-time and time-varying nonlinear systems by comparing the properties in pairs and using examples. We also demonstrate a time-varying smooth Lyapunov function characterization for each of these convergence notions, and, with appropriate assumptions, we provide several sufficient conditions to establish relationships between these properties in terms of Lyapunov functions.</description><subject>Asymptotic stability</subject><subject>Contraction analysis</subject><subject>Convergence</subject><subject>convergent dynamics</subject><subject>Discrete time systems</subject><subject>Dynamic stability</subject><subject>incremental stability</subject><subject>Liapunov functions</subject><subject>Lyapunov methods</subject><subject>Nonlinear systems</subject><subject>Properties (attributes)</subject><subject>Stability analysis</subject><subject>Stability criteria</subject><subject>Time-varying systems</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kE1Lw0AQhhdRsFbvgpeA59Tdyexm11uJ9QOKCua-JJuJpLTZupsK_femtHgaXuZ5Z-Bh7FbwmRDcPJTzYgZc6Bno3BgpzthESKlTkJCdswkfV6kBrS7ZVYyrMSpEMWGPhe9_KXxT7yj5DH5LYegoJq0PyVMXXaCB0rLbUPLu-3XXUxWSr30caBOv2UVbrSPdnOaUlc-LsnhNlx8vb8V8mTowYkgzh9Jxx41CBzxXDWonqlbUQBq5MG3dNNhkhmpjam2cJA6AqCgHdITZlN0fz26D_9lRHOzK70I_frQAKpeoFOqR4kfKBR9joNZuQ7epwt4Kbg-C7CjIHgTZk6CxcnesdET0j2sJCnKT_QHAkmCa</recordid><startdate>20190801</startdate><enddate>20190801</enddate><creator>Tran, Duc N.</creator><creator>Ruffer, Bjorn S.</creator><creator>Kellett, Christopher M.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0001-5028-4978</orcidid><orcidid>https://orcid.org/0000-0002-8309-6807</orcidid><orcidid>https://orcid.org/0000-0001-8180-9773</orcidid></search><sort><creationdate>20190801</creationdate><title>Convergence Properties for Discrete-Time Nonlinear Systems</title><author>Tran, Duc N. ; Ruffer, Bjorn S. ; Kellett, Christopher M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c291t-3c45c0c0964c2076d48c1af1b2e84019fbdd4d39eb99b89c5e022446e724ce43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Asymptotic stability</topic><topic>Contraction analysis</topic><topic>Convergence</topic><topic>convergent dynamics</topic><topic>Discrete time systems</topic><topic>Dynamic stability</topic><topic>incremental stability</topic><topic>Liapunov functions</topic><topic>Lyapunov methods</topic><topic>Nonlinear systems</topic><topic>Properties (attributes)</topic><topic>Stability analysis</topic><topic>Stability criteria</topic><topic>Time-varying systems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Tran, Duc N.</creatorcontrib><creatorcontrib>Ruffer, Bjorn S.</creatorcontrib><creatorcontrib>Kellett, Christopher M.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>IEEE transactions on automatic control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Tran, Duc N.</au><au>Ruffer, Bjorn S.</au><au>Kellett, Christopher M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Convergence Properties for Discrete-Time Nonlinear Systems</atitle><jtitle>IEEE transactions on automatic control</jtitle><stitle>TAC</stitle><date>2019-08-01</date><risdate>2019</risdate><volume>64</volume><issue>8</issue><spage>3415</spage><epage>3422</epage><pages>3415-3422</pages><issn>0018-9286</issn><eissn>1558-2523</eissn><coden>IETAA9</coden><abstract>Three similar convergence notions are considered. Two of them are the long established notions of convergent dynamics and incremental stability. The other is the more recent notion of contraction analysis. All three convergence notions require that all solutions of a system converge to each other. In this note, we investigate the differences between these convergence properties for discrete-time and time-varying nonlinear systems by comparing the properties in pairs and using examples. 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| language | eng |
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| subjects | Asymptotic stability Contraction analysis Convergence convergent dynamics Discrete time systems Dynamic stability incremental stability Liapunov functions Lyapunov methods Nonlinear systems Properties (attributes) Stability analysis Stability criteria Time-varying systems |
| title | Convergence Properties for Discrete-Time Nonlinear Systems |
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