Geodesic
On the Stability of Hybrid Homogeneous Systems
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 5 (2010), pp. 24-32

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The hybrid system consisting of the family of subsystems with homogeneous right-hand sides and a switching law is considered. It is assumed that the zero solution of each subsystem is asymptotically stable. By the use of the Lyapunov functions method, the classes of admissible switching laws are determined under which the corresponding hybrid system is also asymptotically stable. The region of asymptotic stability of the zero solution is investigated.
Keywords: switched systems, stability, homogeneous systems, Lyapunov functions, region of asymptotic stability. 
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     author = {A. Yu. Aleksandrov and A. V. Platonov},
     title = {On the {Stability} of {Hybrid} {Homogeneous} {Systems}},
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A. Yu. Aleksandrov; A. V. Platonov. On the Stability of Hybrid Homogeneous Systems. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 5 (2010), pp. 24-32. http://geodesic.mathdoc.fr/item/VSGTU_2010_5_a2/