Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions

Andrea Bacciotti; Francesca Ceragioli

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 4, page 361-376
  • ISSN: 1292-8119

Abstract

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We study stability and stabilizability properties of systems with discontinuous righthand side (with solutions intended in Filippov's sense) by means of locally Lipschitz continuous and regular Lyapunov functions. The stability result is obtained in the more general context of differential inclusions. Concerning stabilizability, we focus on systems affine with respect to the input: we give some sufficient conditions for a system to be stabilized by means of a feedback law of the Jurdjevic-Quinn type.


How to cite

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Bacciotti, Andrea, and Ceragioli, Francesca. " Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions." ESAIM: Control, Optimisation and Calculus of Variations 4 (2010): 361-376. <http://eudml.org/doc/116570>.

@article{Bacciotti2010,
abstract = { We study stability and stabilizability properties of systems with discontinuous righthand side (with solutions intended in Filippov's sense) by means of locally Lipschitz continuous and regular Lyapunov functions. The stability result is obtained in the more general context of differential inclusions. Concerning stabilizability, we focus on systems affine with respect to the input: we give some sufficient conditions for a system to be stabilized by means of a feedback law of the Jurdjevic-Quinn type.
},
author = {Bacciotti, Andrea, Ceragioli, Francesca},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Stability; stabilization; Clarke gradient; Lyapunov functions; LaSalle principle.; stability; stabilizability; differential inclusions; Jurdevic-Quinn type; LaSalle principle},
language = {eng},
month = {3},
pages = {361-376},
publisher = {EDP Sciences},
title = { Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions},
url = {http://eudml.org/doc/116570},
volume = {4},
year = {2010},
}

TY - JOUR
AU - Bacciotti, Andrea
AU - Ceragioli, Francesca
TI - Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 4
SP - 361
EP - 376
AB - We study stability and stabilizability properties of systems with discontinuous righthand side (with solutions intended in Filippov's sense) by means of locally Lipschitz continuous and regular Lyapunov functions. The stability result is obtained in the more general context of differential inclusions. Concerning stabilizability, we focus on systems affine with respect to the input: we give some sufficient conditions for a system to be stabilized by means of a feedback law of the Jurdjevic-Quinn type.

LA - eng
KW - Stability; stabilization; Clarke gradient; Lyapunov functions; LaSalle principle.; stability; stabilizability; differential inclusions; Jurdevic-Quinn type; LaSalle principle
UR - http://eudml.org/doc/116570
ER -

References

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  19. E.P. Ryan, An Integral Invariance Principle for Differential Inclusions with Applications in Adaptive Control. SIAM J. Control36 (1998) 960-980.  Zbl0911.93046
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