Abstract
ABSTRACT In this paper the control system described by the ordinary nonlinear differential equation is considered. The admissible control functions are chosen from the closed ball of radius r in the space L p , p ∈ [ 1 , ∞ ] , centred at the origin. The behaviour of the set of trajectories at p = 1 is studied. It is proved that the set of trajectories is the Hausdorff right upper semicontinuous and Vietoris right lower semicontinuous at p = 1. It is illustrated that it is not Hausdorff right lower semicontinuous at p = 1.
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