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Geometry of the Limit Sets of Linear Switched Systems

Abstract : The paper is concerned with asymptotic stability properties of linear switched systems. Under the hypothesis that all the subsystems share a non strict quadratic Lyapunov function, we provide a large class of switching signals for which a large class of switched systems are asymptotically stable. For this purpose we define what we call non chaotic inputs, which generalize the different notions of inputs with dwell time. Next we turn our attention to the behaviour for possibly chaotic inputs. To finish we give a sufficient condition for a system composed of a pair of Hurwitz matrices to be asymptotically stable for all inputs.
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https://hal.archives-ouvertes.fr/hal-00475844
Contributor : Philippe Jouan Connect in order to contact the contributor
Submitted on : Friday, April 23, 2010 - 10:31:23 AM
Last modification on : Tuesday, October 19, 2021 - 4:13:32 PM
Long-term archiving on: : Tuesday, September 28, 2010 - 12:45:36 PM

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  • HAL Id : hal-00475844, version 1
  • ARXIV : 1004.5302

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Moussa Balde, Philippe Jouan. Geometry of the Limit Sets of Linear Switched Systems. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2011, 49 (3), pp.1048-1063. ⟨hal-00475844⟩

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