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On correctness of probabilistic stabilization

  • Stability of Systems
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Abstract

Consideration is given to the controlled object with aftereffect under indefinite and stochastic noises. The problem of feedback stabilization with probabilistic actions is discussed. Noises in the form of retarded actions of the motion history are admitted; also, the control of retarded actions of the motion history is tolerated. The paper is based on the Lyapunov stability theory [1] modernized for hereditary and stochastic systems. The approach typical of the control theory in the presence of a conflict or uncertainty is used.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia

    A. N. Kotel’nikova & N. N. Krasovskii

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  1. A. N. Kotel’nikova
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  2. N. N. Krasovskii
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Additional information

Original Russian Text © A.N. Kotel’nikova, N.N. Krasovskii, 2007, published in Avtomatika i Telemekhanika, 2007, No. 10, pp. 106–124.

This work was supported by the Russian Foundation for Basic Research, project no. 06-01-00436 and the Russian Federation President Grant “State Support for Leading Scientific Schools,” project no. NSh-8512.2006.1.

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Kotel’nikova, A.N., Krasovskii, N.N. On correctness of probabilistic stabilization. Autom Remote Control 68, 1826–1843 (2007). https://doi.org/10.1134/S0005117907100104

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  • DOI: https://doi.org/10.1134/S0005117907100104

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