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Control Systems of Variable Structure. Attainability Sets and Integral Funnels

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We consider a nonlinear control system in a finite-dimensional Euclidean space and on a finite time interval. The system varies over some less time interval, and the differential equation describing the system is replaced with some other differential equation. As a result, a new control system appears on the initial time interval. We study how much the integral funnel of the system is changed under such a replacement. We obtain the upper estimate for the Hausdorff distance between the integral funnels of differential inclusions related to the initial and varied systems.

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Authors and Affiliations

  1. N. N. Krasovskii Institute of Mathematics and Mechanics, UB RAS, 16, Kovalevskaya St, Ekaterinburg, 620090, Russia

    V. N. Ushakov, V. I. Ukhobotov, A. V. Ushakov & I. V. Izmest’ev

  2. Chelyabinsk State University, 129, Brat’ev Kashirinyh St, Chelyabinsk, 454021, Russia

    V. I. Ukhobotov & I. V. Izmest’ev

Authors
  1. V. N. Ushakov
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  2. V. I. Ukhobotov
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  3. A. V. Ushakov
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  4. I. V. Izmest’ev
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Corresponding author

Correspondence to I. V. Izmest’ev.

Additional information

Translated from Problemy Matematicheskogo Analiza 113, 2022, pp. 101-112.

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Ushakov, V.N., Ukhobotov, V.I., Ushakov, A.V. et al. Control Systems of Variable Structure. Attainability Sets and Integral Funnels. J Math Sci 260, 820–832 (2022). https://doi.org/10.1007/s10958-022-05730-1

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  • DOI: https://doi.org/10.1007/s10958-022-05730-1

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