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On existence conditions for a two-point oscillating periodic solution in an non-autonomous relay system with a Hurwitz matrix

  • Nonlinear Systems
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Abstract

We consider a system of differential equations with relay nonlinearity and an external continuous periodic influence. For system parameters, we obtain sufficient existence and uniqueness conditions for a two-point oscillating solution with given period in case of a Hurwitz system matrix. With exact analytic approaches, we find time moments and switching points in the phase space of the image point for a solution whose period is a multiple of the period of external disturbances. We obtain conditions on system parameters for which a solution in the considered class is asymptotically-orbital stable.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    V. V. Yevstafyeva

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  1. V. V. Yevstafyeva
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Correspondence to V. V. Yevstafyeva.

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Original Russian Text © V.V. Yevstafyeva, 2015, published in Avtomatika i Telemekhanika, 2015, No. 6, pp. 42–56.

This paper was recommended for publication by A.M. Krasnosel’skii, a member of the Editorial Board

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Yevstafyeva, V.V. On existence conditions for a two-point oscillating periodic solution in an non-autonomous relay system with a Hurwitz matrix. Autom Remote Control 76, 977–988 (2015). https://doi.org/10.1134/S000511791506003X

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  • DOI: https://doi.org/10.1134/S000511791506003X

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