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On exact controllability of variational discrete systems

✍ Scribed by Adina Luminiţa Sasu

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
366 KB
Volume
23
Category
Article
ISSN
0893-9659

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✦ Synopsis

a b s t r a c t Let X , U be two Banach spaces, let Θ be a metric space and let σ be a flow on Θ. For A ∈ ∞ (Θ, B(X)) and B ∈ ∞ (Θ, B(U, X )), we consider the variational discrete system with control

where x : Θ → S(X) and u ∈ p (N, U). We prove that if the discrete cocycle associated with the system (A, B) is surjective and the variational discrete system (A, B) is completely stabilizable, then (A, B) is exactly controllable. By illustrative examples we show that our hypotheses cannot be dropped and also we study the validity of the converse implication.

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