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Extension of the Concept of Invariance and Statistically Weakly Invariant Sets of Controllable Systems

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Abstract

We continue the study of statistically invariant and statistically weakly invariant sets with respect to controllable systems and differential inclusions launched by Prof. E. L. Tonkov. We examine properties of such statistical characteristics as the lower freq*(đťś‘) and upper freq*(đťś‘) relative frequencies of hitting a solution đťś‘(t) of a differential inclusion in a prescribed set. We obtain estimates and conditions of coincidence of these characteristics for functions whose difference tends to zero at infinity. We also present conditions of statistically weak invariance of a given set of a relatively controllable system.

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Authors and Affiliations

  1. Udmurt State University, Izhevsk, Russia

    Ya. Yu. Larina & L. I. Rodina

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  1. Ya. Yu. Larina
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  2. L. I. Rodina
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Correspondence to Ya. Yu. Larina.

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Dedicated to Professor E. L. Tonkov

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 132, Proceedings of International Symposium “Differential Equations–2016,” Perm, 2016.

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Larina, Y.Y., Rodina, L.I. Extension of the Concept of Invariance and Statistically Weakly Invariant Sets of Controllable Systems. J Math Sci 230, 703–707 (2018). https://doi.org/10.1007/s10958-018-3773-5

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  • DOI: https://doi.org/10.1007/s10958-018-3773-5

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