LMI Conditions for the Stability of Linear Uncertain Polynomially Time-Varying Systems
This technical note investigates the robust stability of uncertain linear time-varying systems with a mode-switch dynamics. Each mode is characterized by a dynamical matrix containing elements whose time behavior over bounded time intervals is described by interval polynomials of arbitrary degree. U...
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| Veröffentlicht in: | IEEE transactions on automatic control 2009-07, Vol.54 (7), p.1705-1709 |
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| container_title | IEEE transactions on automatic control |
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| creator | Jetto, L. Orsini, V. |
| description | This technical note investigates the robust stability of uncertain linear time-varying systems with a mode-switch dynamics. Each mode is characterized by a dynamical matrix containing elements whose time behavior over bounded time intervals is described by interval polynomials of arbitrary degree. Using a quadratic Lyapunov function polynomially depending on time, stability conditions for each mode are stated in terms of linear matrix inequalities (LMIs). The stability conditions of the switching system are stated both in terms of minimum and average dwell time. A salient feature of the technical note is that the single-mode stability conditions given here allow the parameters and their derivatives to take values over arbitrarily large uncertainty sets. |
| doi_str_mv | 10.1109/TAC.2009.2020645 |
| format | Article |
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Each mode is characterized by a dynamical matrix containing elements whose time behavior over bounded time intervals is described by interval polynomials of arbitrary degree. Using a quadratic Lyapunov function polynomially depending on time, stability conditions for each mode are stated in terms of linear matrix inequalities (LMIs). The stability conditions of the switching system are stated both in terms of minimum and average dwell time. A salient feature of the technical note is that the single-mode stability conditions given here allow the parameters and their derivatives to take values over arbitrarily large uncertainty sets.</description><identifier>ISSN: 0018-9286</identifier><identifier>EISSN: 1558-2523</identifier><identifier>DOI: 10.1109/TAC.2009.2020645</identifier><identifier>CODEN: IETAA9</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Applied sciences ; Computer science; control theory; systems ; Control system analysis ; Control theory. 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Each mode is characterized by a dynamical matrix containing elements whose time behavior over bounded time intervals is described by interval polynomials of arbitrary degree. Using a quadratic Lyapunov function polynomially depending on time, stability conditions for each mode are stated in terms of linear matrix inequalities (LMIs). The stability conditions of the switching system are stated both in terms of minimum and average dwell time. A salient feature of the technical note is that the single-mode stability conditions given here allow the parameters and their derivatives to take values over arbitrarily large uncertainty sets.</description><subject>Applied sciences</subject><subject>Computer science; control theory; systems</subject><subject>Control system analysis</subject><subject>Control theory. Systems</subject><subject>Covariance matrix</subject><subject>Derivatives</subject><subject>Dwell time</subject><subject>Dynamic tests</subject><subject>Dynamical systems</subject><subject>Dynamics</subject><subject>Exact sciences and technology</subject><subject>Linear matrix inequalities</subject><subject>Linear matrix inequalities (LMIs)</subject><subject>Lyapunov functions</subject><subject>Lyapunov method</subject><subject>Polynomials</subject><subject>Robust stability</subject><subject>robust stability analysis</subject><subject>Stability</subject><subject>Switching</subject><subject>Switching systems</subject><subject>Time varying systems</subject><subject>Uncertain systems</subject><subject>Uncertainty</subject><subject>White noise</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kc1rGzEUxEVIII6Te6AXUWh72kSfK-kYTNoGXBqI7auQ10-twq6USuvD_veVscmhh14kxPvNPEaD0C0ld5QSc796WNwxQkw9GGmFPEMzKqVumGT8HM0IoboxTLeX6KqU1_pshaAztFn-eMKLFHdhDCkW7FPG42_AL6Pbhj6ME04eL0MEl_E6dpBHFyJ-Tv0U0xBc3094FQZoNi5PIf7CL1MZYSjX6MK7vsDN6Z6j9dfH1eJ7s_z57WnxsGw6rvnYSE-kUYxp7pRnkgsnDCPb7Y4YDUpp8MrvpDPMCGWI6YB2brtrNadUQc3A5-jL0fctpz97KKMdQumg712EtC9WK0kEo6Kt5Of_klwYw02rKvjxH_A17XOsKaxuKTNMGV4hcoS6nErJ4O1bDkP9A0uJPfRhax_20Ic99VEln06-rnSu99nFLpR3HaOHVOaw_8ORCwDwPpbVU2jO_wKvvZGA</recordid><startdate>20090701</startdate><enddate>20090701</enddate><creator>Jetto, L.</creator><creator>Orsini, V.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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Systems</topic><topic>Covariance matrix</topic><topic>Derivatives</topic><topic>Dwell time</topic><topic>Dynamic tests</topic><topic>Dynamical systems</topic><topic>Dynamics</topic><topic>Exact sciences and technology</topic><topic>Linear matrix inequalities</topic><topic>Linear matrix inequalities (LMIs)</topic><topic>Lyapunov functions</topic><topic>Lyapunov method</topic><topic>Polynomials</topic><topic>Robust stability</topic><topic>robust stability analysis</topic><topic>Stability</topic><topic>Switching</topic><topic>Switching systems</topic><topic>Time varying systems</topic><topic>Uncertain systems</topic><topic>Uncertainty</topic><topic>White noise</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Jetto, L.</creatorcontrib><creatorcontrib>Orsini, V.</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>Pascal-Francis</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><collection>ANTE: Abstracts in New Technology & Engineering</collection><jtitle>IEEE transactions on automatic control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Jetto, L.</au><au>Orsini, V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>LMI Conditions for the Stability of Linear Uncertain Polynomially Time-Varying Systems</atitle><jtitle>IEEE transactions on automatic control</jtitle><stitle>TAC</stitle><date>2009-07-01</date><risdate>2009</risdate><volume>54</volume><issue>7</issue><spage>1705</spage><epage>1709</epage><pages>1705-1709</pages><issn>0018-9286</issn><eissn>1558-2523</eissn><coden>IETAA9</coden><abstract>This technical note investigates the robust stability of uncertain linear time-varying systems with a mode-switch dynamics. 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| source | IEEE Electronic Library (IEL) |
| subjects | Applied sciences Computer science control theory systems Control system analysis Control theory. Systems Covariance matrix Derivatives Dwell time Dynamic tests Dynamical systems Dynamics Exact sciences and technology Linear matrix inequalities Linear matrix inequalities (LMIs) Lyapunov functions Lyapunov method Polynomials Robust stability robust stability analysis Stability Switching Switching systems Time varying systems Uncertain systems Uncertainty White noise |
| title | LMI Conditions for the Stability of Linear Uncertain Polynomially Time-Varying Systems |
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