Weak Convergence of Set-Valued Functions and Control

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Abstract
Weak convergence on the space of integrably bounded set-valued functions is defined. Generalizations of results of weak convergence of real-valued integrable functions are obtained in the set-valued case. The results are applied to the characterization of the continuous dependence of the attainable set of a linear control system on the restraint set. We show that the weak convergence of the restraint set is a sufficient condition for the uniform convergence of the attainable set, and under the additional condition of uniform integrability the weak convergence is also a necessary condition.

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