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

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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 assumed that subsystems are homogeneous with homogeneity degrees less than one, and zero solutions of all subsystems are asymptotically stable. Using the Lyapunov direct method and the method of differential inequalities, we determine classes of switching laws providing prescribed estimates of domains of attraction for zero solutions of the corresponding hybrid systems. The developed approaches are used for the stabilization of a double integrator.

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Authors and Affiliations

  1. St. Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg, 199034, Russia

    A. Yu. Aleksandrov, E. B. Aleksandrova & A. V. Platonov

  2. Beijing University of Technology, ul. Pingleyuan 100, Chaoyang District, Beijing, 100124, China

    Y. Chen

Authors
  1. A. Yu. Aleksandrov
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  2. E. B. Aleksandrova
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  3. A. V. Platonov
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  4. Y. Chen
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Corresponding author

Correspondence to A. Yu. Aleksandrov.

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Original Russian Text © A.Yu. Aleksandrov, E.B. Aleksandrova, A.V. Platonov, Y. Chen, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 8, pp. 3–16.

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Aleksandrov, A.Y., Aleksandrova, E.B., Platonov, A.V. et al. Estimate of the attraction domain for a class of nonlinear switched systems. Russ Math. 61, 1–12 (2017). https://doi.org/10.3103/S1066369X17080011

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  • DOI: https://doi.org/10.3103/S1066369X17080011

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