Stability Analysis of Implicit Polynomial Systems
This technical note develops a robust stability analysis method for a class of implicit polynomial systems subject to uncertain constant parameters. A polynomial (with respect to the state and uncertain parameters) Lyapunov function is computed to assess the robust local stability of the system and...
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| Published in | IEEE transactions on automatic control Vol. 54; no. 5; pp. 1012 - 1018 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
IEEE
01.05.2009
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0018-9286 1558-2523 |
| DOI | 10.1109/TAC.2009.2017145 |
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| Abstract | This technical note develops a robust stability analysis method for a class of implicit polynomial systems subject to uncertain constant parameters. A polynomial (with respect to the state and uncertain parameters) Lyapunov function is computed to assess the robust local stability of the system and to provide a robust estimate of the domain of attraction. The results are given in terms of linear matrix inequalities that are affinely dependent on the system state and uncertain parameters. Numerical examples illustrate the effectiveness of the developed approach. |
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| AbstractList | This technical note develops a robust stability analysis method for a class of implicit polynomial systems subject to uncertain constant parameters. A polynomial (with respect to the state and uncertain parameters) Lyapunov function is computed to assess the robust local stability of the system and to provide a robust estimate of the domain of attraction. The results are given in terms of linear matrix inequalities that are affinely dependent on the system state and uncertain parameters. Numerical examples illustrate the effectiveness of the developed approach. |
| Author | Coutinho, D.F. Trofino, A. de Souza, C.E. |
| Author_xml | – sequence: 1 givenname: D.F. surname: Coutinho fullname: Coutinho, D.F. organization: Group of Autom. & Syst., PUC-RS, Porto Alegre – sequence: 2 givenname: C.E. surname: de Souza fullname: de Souza, C.E. organization: Dept. of Syst. & Control, Lab. Nac. de Comput. Cientfficao-LNCC/MCT, Petropolis – sequence: 3 givenname: A. surname: Trofino fullname: Trofino, A. organization: Dept. of Autom. & Syst., Univ. Fed. de Santa Catarina, Florianopolis |
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| Cites_doi | 10.4171/017 10.1109/CDC.2003.1272591 10.1016/j.automatica.2006.11.005 10.1137/1.9781611970777 10.1109/TAC.2004.831152 10.1007/BFb0110624 10.1002/rnc.950 10.1109/TAC.2002.802737 10.1109/9.940924 10.1007/10997703_2 10.1109/ACC.2000.879262 10.1002/rnc.1207 10.1016/0005-1098(96)00071-4 10.1007/BF01600184 |
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| References | ref13 murray (ref1) 1994 ref12 ref15 huang (ref20) 1999 ref21 el ghaoui (ref10) 1996; 32 ref2 wang (ref9) 2006 ref17 ref16 ref19 papachristodoulou (ref14) 2005 ref8 ref7 khalil (ref18) 1996 parrilo (ref11) 1999 ref4 xu (ref6) 2006 ref5 kumar (ref3) 1999 papachristodoulou (ref22) 2005 |
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| SubjectTerms | Attraction Automatic control Automation Computation Control systems Domain of attraction Estimates Linear matrix inequalities Lyapunov functions Lyapunov method Mathematical models Nonlinear systems parameter-dependent Lyapunov function polynomial systems Polynomials Robust stability Stability Stability analysis State estimation uncertain systems Vectors |
| Title | Stability Analysis of Implicit Polynomial Systems |
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