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Asymptotic stability of uniformly bounded nonlinear switched systems
1. | Université de Rouen, Laboratoire de Mathématiques Raphaël Salem, CNRS, UMR 6085, Avenue de luniversité, BP 12, 76801 Saint-Etienne du Rouvray Cedex, France, France |
  We consider the class of nonchaotic inputs, which generalize the different notions of inputs with dwell-time, and the class of general ones. For each of them we provide some sufficient conditions for asymptotic stability in terms of the geometry of certain sets.
References:
[1] |
A. Yu. Aleksandrov, A. A. Kosov and A. V. Platonov, On the asymptotic stability of switched homogeneous systems,, Systems & Control Letters, 61 (2012), 127.
doi: 10.1016/j.sysconle.2011.10.008. |
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doi: 10.1137/100793153. |
[5] |
M. Balde and P. Jouan, Stability of linear switched systems with quadratic bounds and observability of bilinear systems, preprint,, , (). Google Scholar |
[6] |
U. Boscain, G. Charlot and M. Sigalotti, Stability of planar nonlinear switched systems,, Discrete and Continuous Dynamical Systems, 15 (2006), 415.
doi: 10.3934/dcds.2006.15.415. |
[7] |
J. Carr, "Applications of Centre Manifold Theory,", Applied Mathematical Sciences, (1981).
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[8] |
J. Hespanha, Uniform stability of switched linear systems: Extensions of lasalle's invariance principle,, IEEE Trans. Automat. Control, 49 (2004), 470.
doi: 10.1109/TAC.2004.825641. |
[9] |
J. L. Mancilla-Aguilar and R. A. García, An extension of lasalle's invariance principle for switched systems,, Systems & Control Letters, 55 (2006), 376.
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C. Marle, "Systèmes Dynamiques: Une Introduction,", Ellipses, (2003). Google Scholar |
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U. Serres, J.-C. Vivalda and P. Riedinger, On the convergence of linear switched systems,, IEEE Trans. Automat. Control, 56 (2011), 320.
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[12] |
E. D. Sontag, "Mathematical Control Theory. Deterministic Finite-Dimensional Systems,", 2nd edition, (1998).
|
show all references
References:
[1] |
A. Yu. Aleksandrov, A. A. Kosov and A. V. Platonov, On the asymptotic stability of switched homogeneous systems,, Systems & Control Letters, 61 (2012), 127.
doi: 10.1016/j.sysconle.2011.10.008. |
[2] |
D. Angeli, B. Ingalls, E. D. Sontag and Y. Wang, Uniform global asymptotic stability of differential inclusions,, Journal of Dynamical and Control Systems, 10 (2004), 391.
doi: 10.1023/B:JODS.0000034437.54937.7f. |
[3] |
A. Bacciotti and L. Mazzi, An invariance principle for nonlinear switched systems,, Systems & Control Letters, 54 (2005), 1109.
doi: 10.1016/j.sysconle.2005.04.003. |
[4] |
M. Balde and P. Jouan, Geometry of the limit sets of linear switched systems,, SIAM J. Optimization and Control, 49 (2011), 1048.
doi: 10.1137/100793153. |
[5] |
M. Balde and P. Jouan, Stability of linear switched systems with quadratic bounds and observability of bilinear systems, preprint,, , (). Google Scholar |
[6] |
U. Boscain, G. Charlot and M. Sigalotti, Stability of planar nonlinear switched systems,, Discrete and Continuous Dynamical Systems, 15 (2006), 415.
doi: 10.3934/dcds.2006.15.415. |
[7] |
J. Carr, "Applications of Centre Manifold Theory,", Applied Mathematical Sciences, (1981).
|
[8] |
J. Hespanha, Uniform stability of switched linear systems: Extensions of lasalle's invariance principle,, IEEE Trans. Automat. Control, 49 (2004), 470.
doi: 10.1109/TAC.2004.825641. |
[9] |
J. L. Mancilla-Aguilar and R. A. García, An extension of lasalle's invariance principle for switched systems,, Systems & Control Letters, 55 (2006), 376.
doi: 10.1016/j.sysconle.2005.07.009. |
[10] |
C. Marle, "Systèmes Dynamiques: Une Introduction,", Ellipses, (2003). Google Scholar |
[11] |
U. Serres, J.-C. Vivalda and P. Riedinger, On the convergence of linear switched systems,, IEEE Trans. Automat. Control, 56 (2011), 320.
doi: 10.1109/TAC.2010.2054950. |
[12] |
E. D. Sontag, "Mathematical Control Theory. Deterministic Finite-Dimensional Systems,", 2nd edition, (1998).
|
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