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International Journal of Control Volume 82, 2009 - Issue 10
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Original Articles

A note on stability conditions for planar switched systems

Moussa Balde LMDAN-LGDA Département de Mathématiques et Informatique, UCAD, Dakar-Fann, Senegal
,
Ugo Boscain CMAP École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau, France
&
Paolo Mason Istituto per le Applicazioni del Calcolo Mauro Picone - CNR Viale del Policlinico, 137 - 00161 Roma, Italy; Laboratoire des signaux et systémes, Université Paris-Sud, CNRS, Supélec, 91192 Gif-Sur-Yvette, FranceCorrespondence[email protected]
Pages 1882-1888 | Received 22 Sep 2008, Accepted 06 Feb 2009, Published online: 06 Aug 2009

References

  • Balde , M and Boscain , U . 2008 . Stability of Planar Switched Systems: The Nondiagonalizable Case . Communications on Pure and Applied Analysis , 7 : 1 – 21 .
  • Blanchini , F and Miani , S . 1999 . A New Class of Universal Lyapunov Functions for the Control of Uncertain Linear Systems . IEEE Transactions on Automatic Control , 44 : 641 – 647 .
  • Boscain , U . 2002 . Stability of Planar Switched Systems: The Linear Single Input Case . SIAM Journal of Control Optimization , 41 : 89 – 112 . (electronic)
  • Dayawansa , WP and Martin , CF . 1999 . A Converse Lyapunov Theorem for a Class of Dynamical Systems which Undergo Switching . IEEE Transactions on Automatic Control , 44 : 751 – 760 .
  • Liberzon , D . 2003 . Switching in Systems and Control. Systems & Control: Foundations & Applications , Boston, MA : Birkhäuser Boston Inc .
  • Margaliot , M and Langholz , G . 2003 . Necessary and Sufficient Conditions for Absolute Stability: The Case of Second-order Systems . IEEE Transactions on Circuits and Systems , 50 : 227 – 234 .
  • Mason , P , Boscain , U and Chitour , Y . 2006 . Common Polynomial Lyapunov Functions for Linear Switched Systems . SIAM Journal of Control and Optimization , 45 : 226 – 245 . (electronic)
  • Molchanov , AP and Pyatnitskiĭ , ES . 1986a . Lyapunov Functions that Define Necessary and Sufficient Conditions for Absolute Stability of Nonlinear Nonstationary Control Systems . I. Automation Remote Control , 47 : 343 – 354 .
  • Molchanov , AP and Pyatnitskiĭ , ES . 1986b . Lyapunov Functions that Define Necessary and Sufficient Conditions for Absolute Stability of Nonlinear Nonstationary Control Systems . II. Automation and Remote Control , 47 : 443 – 451 .
  • Shorten , R and Narendra , K . 1999 . Necessary and Sufficient Conditions for the Existence of a Common Quadratic Lyapunov Function for Two Stable Second-Order Linear Time-invariant Systems . Proceedings 1999, American Control Conference , : 1410 – 1414 .

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