Abstract
The property of so-called uniform covering is proved for a family of linear operators generated
by a differential equation linear with respect to functional parameters. Using this fact, a uniform
estimate of the distance to the level set of a nonlinear operator is obtained on a broader set than
a neighborhood of the examined point in a Banach space. This allows to prove an approximation
theorem for a system with sliding mode controls and endpoint state constraints.
Key words:
nonlinear operator, covering, weak-* topology, sliding modes.
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