Geodesic
On properties of characteristics of attainability set for a control system
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 46 (2015) no. 2, pp. 216-227

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We continue to study the characteristics of a control system, which reflect uniform staying the attainability set of the system in a given set $\mathfrak M\doteq\bigl\{(t,x)\in [0,+\infty)\times\mathbb R^n: x\in M(t)\bigr\}$ during a finite time interval. In terms of Lyapunov functions and Clarke's derivative, we obtain conditions under which relative frequencies of absorption of attainability set for the control system can be estimated by similar characteristics defined for differential equations. We prove a theorem about evaluating and calculating of the relative frequencies for some multivalued functions. We get estimation for different characteristics of Bohr almost periodic functions. We show examples of calculations and estimations for the relative frequencies of staying graphs of functions in a given set.
Keywords: controllable systems, differential inclusions, attainability set, almost periodic functions. 
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     author = {A. H. Hammady},
     title = {On properties of characteristics of attainability set for a control system},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
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     publisher = {mathdoc},
     volume = {46},
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     url = {http://geodesic.mathdoc.fr/item/IIMI_2015_46_2_a26/}
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A. H. Hammady. On properties of characteristics of attainability set for a control system. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 46 (2015) no. 2, pp. 216-227. http://geodesic.mathdoc.fr/item/IIMI_2015_46_2_a26/