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Solution tubes to differential inclusions within a collection of sets

Quincampoix M., Veliov V.

Control and Cybernetics

2002

Vol. 31, no 3

847-862

This paper develops the theory of solution tubes to differential inclusions (uncertain systems) within a prescribed collection of sets. The notion is defined as a minimal invariant tube with values in the collection. Under certain requirements for the collection we prove existence and Lipschitz-like stability of the solution tubes. The theory is relevant to problems of systems estimation in the context of control or differential games.