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 Model. Anal. Inform. Sist., 2013, Volume 20, Number 5, Pages 62–77 (Mi mais332)

Statistical Characteristics of Control Systems, Arising in Various Models of Natural Sciences

Y. Y. Larina, L. I. Rodina

Udmurt State University, Universitetskaya St., 1, bld. 4, off. 206, Izhevsk, 426034, Russia

Abstract: We continue the study of extending the concept of invariance sets relative to control systems and differential inclusions. This expansion consists in studying statistically invariant sets and statistical characteristics of the attainability set of control systems. In this work, we obtain conditions for the statistical invariance and investigate the properties of the statistical characteristics of control systems with periodic coefficients. It is shown that the property of statistical invariancy is closely connected with the property of admissibility of periodic processes for linear control systems. The admissibility means that for any periodic control from the fixed set there exists a unique periodic solution which is in the given set of the phase space. The results of the work can be applied while finding the statistical characteristics arising in various models of biology, chemistry, economy.

Keywords: control systems, differential inclusions, invariant and statistically invariant sets.

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UDC: 517.911+517.935

Citation: Y. Y. Larina, L. I. Rodina, “Statistical Characteristics of Control Systems, Arising in Various Models of Natural Sciences”, Model. Anal. Inform. Sist., 20:5 (2013), 62–77

Citation in format AMSBIB
\Bibitem{LarRod13} \by Y.~Y.~Larina, L.~I.~Rodina \paper Statistical Characteristics of Control Systems, Arising in Various Models of Natural Sciences \jour Model. Anal. Inform. Sist. \yr 2013 \vol 20 \issue 5 \pages 62--77 \mathnet{http://mi.mathnet.ru/mais332} 

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This publication is cited in the following articles:
1. Ya. Yu. Larina, L. I. Rodina, “Statistical characteristics of continuous functions and statistically weakly invariant sets of controllable system”, Russian Math. (Iz. VUZ), 61:2 (2017), 28–35
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