Piecewise structure of Lyapunov functions and densely checked decrease conditions for hybrid systems
We propose a class of locally Lipschitz functions with piecewise structure for use as Lyapunov functions for hybrid dynamical systems. Subject to some regularity of the dynamics, we show that Lyapunov inequalities can be checked only on a dense set and thus we avoid checking them at points of nondif...
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| Published in | Mathematics of control, signals, and systems Vol. 33; no. 1; pp. 123 - 149 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
London
Springer London
01.03.2021
Springer Nature B.V Springer Verlag |
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| ISSN | 0932-4194 1435-568X |
| DOI | 10.1007/s00498-020-00273-9 |
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| Abstract | We propose a class of locally Lipschitz functions with piecewise structure for use as Lyapunov functions for hybrid dynamical systems. Subject to some regularity of the dynamics, we show that Lyapunov inequalities can be checked only on a dense set and thus we avoid checking them at points of nondifferentiability of the Lyapunov function. Connections to other classes of locally Lipschitz or piecewise regular functions are also discussed, and applications to hybrid dynamical systems are included. |
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| AbstractList | We propose a class of locally Lipschitz functions with piecewise structure for use as Lyapunov functions for hybrid dynamical systems. Subject to some regularity of the dynamics, we show that Lyapunov inequalities can be checked only on a dense set and thus we avoid checking them at points of nondifferentiability of the Lyapunov function. Connections to other classes of locally Lipschitz or piecewise regular functions are also discussed, and applications to hybrid dynamical systems are included. |
| Author | Goebel, Rafal Della Rossa, Matteo Zaccarian, Luca Tanwani, Aneel |
| Author_xml | – sequence: 1 givenname: Matteo orcidid: 0000-0002-5591-5748 surname: Della Rossa fullname: Della Rossa, Matteo email: mdellaro@laas.fr organization: LAAS-CNRS, Université de Toulouse – sequence: 2 givenname: Rafal surname: Goebel fullname: Goebel, Rafal organization: Department of Statistics and Mathematics, Loyola University – sequence: 3 givenname: Aneel surname: Tanwani fullname: Tanwani, Aneel organization: LAAS-CNRS, Université de Toulouse – sequence: 4 givenname: Luca surname: Zaccarian fullname: Zaccarian, Luca organization: LAAS-CNRS, Université de Toulouse, Department of Industrial Engineering, University of Trento |
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| Cites_doi | 10.1007/978-1-4614-4340-7 10.1080/00029890.1983.11971150 10.1007/978-3-642-02431-3 10.1137/1.9781611971309 10.1109/TAC.2006.872764 10.1006/jdeq.1998.3476 10.1109/9.754812 10.1109/TAC.2014.2304397 10.1109/TAC.2011.2114436 10.1007/0-8176-4470-9_6 10.1109/9.317122 10.1137/19M1298147 10.1051/cocv:1999113 10.1137/1.9781611970777 10.1051/cocv:2000113 10.1109/MCS.2008.919306 10.1016/0362-546X(90)90005-2 10.1016/j.na.2007.05.022 10.1016/0167-6911(89)90021-2 10.1109/ACC.2005.1470016 10.1002/rnc.1649 10.1137/S0363012993259981 10.1137/090749797 10.1007/PL00009865 10.1016/j.automatica.2007.11.014 10.1016/j.automatica.2020.109123 10.1007/978-94-015-7793-9 10.3934/dcdsb.2012.17.33 10.1007/978-3-642-69512-4 10.1109/9.964694 10.1515/9781400842636 10.1561/2600000017 10.1016/j.automatica.2016.03.018 |
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| Issue | 1 |
| Keywords | Hybrid systems Densely checked conditions Lyapunov analysis Piecewise differentiable functions |
| Language | English |
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| SubjectTerms | Automatic Communications Engineering Control Dynamical Systems Engineering Sciences Hybrid systems Liapunov functions Mathematics Mathematics and Statistics Mechatronics Networks Original Article Robotics Systems Theory |
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| Title | Piecewise structure of Lyapunov functions and densely checked decrease conditions for hybrid systems |
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