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Journal of Mathematical Sciences

, Volume 230, Issue 5, pp 703–707 | Cite as

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

  • Ya. Yu. Larina
  • L. I. Rodina
Article
  • 8 Downloads

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*(𝜑) and upper freq*(𝜑) relative frequencies of hitting a solution 𝜑(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.

Keywords and phrases

controllable system dynamical system attainability set statistical characteristic statistically weakly invariant set 

AMS Subject Classification

34A60 34H05 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Udmurt State UniversityIzhevskRussia

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