Geodesic
Estimate of the attraction domain for a class of nonlinear switched systems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2017), pp. 3-16

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We consider a hybrid dynamical system composed of a family of subsystems of nonlinear differential equations and a switching law which determines the order of their operation. It is supposed that the subsystems are homogeneous with homogeneity degrees less than one, and the zero solutions of all the subsystems are asymptotically stable. Based on the Lyapunov direct method and the differential inequalities method, we derermine classes of switching laws providing prescribed estimates of attraction domains for the zero solutions of the corresponding hybrid systems. The developed approaches are used for the stabilization of a double integrator.
Keywords: switched systems, homogeneous function, the Lyapunov direct method, differential inequalities.
Mots-clés : attraction domain 
@article{IVM_2017_8_a0,
     author = {A. Yu. Aleksandrov and E. B. Aleksandrova and A. V. Platonov and Y. Chen},
     title = {Estimate of the attraction domain for a class of nonlinear switched systems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--16},
     publisher = {mathdoc},
     number = {8},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_8_a0/}
}
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A. Yu. Aleksandrov; E. B. Aleksandrova; A. V. Platonov; Y. Chen. Estimate of the attraction domain for a class of nonlinear switched systems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2017), pp. 3-16. http://geodesic.mathdoc.fr/item/IVM_2017_8_a0/