Geodesic
Extended Lie algebraic stability analysis for switched systems with continuous-time and discrete–time subsystems
International Journal of Applied Mathematics and Computer Science, Tome 17 (2007) no. 4, pp. 447-454.

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We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show that there is a common quadratic Lyapunov-like function for all subsystems and the switched system is exponentially stable under a dwell time scheme. Two numerical examples are provided to demonstrate the result.
Keywords: switched systems, common quadratic Lyapunov functions, Lie algebra, exponential stability, arbitrary switching, dwell time scheme
Mots-clés : układ komutowany, funkcja Lapunowa, algebra Lie'go, stateczność wykładnicza 
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Zhai, G.; Xu, X.; Lin, H.; Liu, D. Extended Lie algebraic stability analysis for switched systems with continuous-time and discrete–time subsystems. International Journal of Applied Mathematics and Computer Science, Tome 17 (2007) no. 4, pp. 447-454. http://geodesic.mathdoc.fr/item/IJAMCS_2007_17_4_a1/

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