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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, Number 8, Pages 3–16 (Mi ivm9264)  
This article is cited in 2 scientific papers (total in 2 papers)

Estimate of the attraction domain for a class of nonlinear switched systems

A. Yu. Aleksandrova, E. B. Aleksandrovaa, A. V. Platonova, Y. Chenb

a St. Petersburg State University, 7/9 Universitetskaya Embankment, St. Petersburg, 199034 Russia
b Beijing University of Technology, 100 Pingleyuan str., Chaoyang District, Beijing, 100124 China
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Abstract: 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, attraction domain, the Lyapunov direct method, differential inequalities.
Funding agency Grant number
Russian Foundation for Basic Research 15-58-53017_ГФЕН_а
16-01-00587_а
National Natural Science Foundation of China 6141101096
61573030
61273006
Received: 24.03.2016
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, Volume 61, Issue 8, Pages 1–12
DOI: https://doi.org/10.3103/S1066369X17080011
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: A. Yu. Aleksandrov, E. B. Aleksandrova, A. V. Platonov, Y. Chen, “Estimate of the attraction domain for a class of nonlinear switched systems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 8, 3–16; Russian Math. (Iz. VUZ), 61:8 (2017), 1–12
Citation in format AMSBIB
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\paper Estimate of the attraction domain for a class of nonlinear switched systems
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\pages 3--16
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\vol 61
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    • This publication is cited in the following 2 articles:
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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