Geodesic
Estimation of statistical characteristics of attainability sets of controllable systems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2013), pp. 20-32

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We study an expansion of the notion of invariance for sets with respect to controllable systems and differential inclusions. Namely, we study statistically invariant sets and statistical characteristics of attainability sets of controllable systems. We obtain a lower bound for the lower relative frequency of the absorption of the attainability set of a system by a given set and establish new sufficient conditions of the statistical invariance of the set with respect to the controllable system. We give examples of the calculation of statistical characteristics for the linear Cauchy problem and a linear controllable system with almost periodic coefficients.
Keywords: controllable systems, dynamical systems, differential inclusions, statistically invariant sets. 
@article{IVM_2013_11_a1,
     author = {L. I. Rodina},
     title = {Estimation of statistical characteristics of attainability sets of controllable systems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {20--32},
     publisher = {mathdoc},
     number = {11},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_11_a1/}
}
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L. I. Rodina. Estimation of statistical characteristics of attainability sets of controllable systems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2013), pp. 20-32. http://geodesic.mathdoc.fr/item/IVM_2013_11_a1/