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Complete controllability of perturbed linear control systems,revisited
Authors:A. Villani
Affiliation:1. Department of Mathematics, University of Messina, Messina, Italy
Abstract:LetL1(I, propn,nM(I, Ropfn,m) be the space of all pairs (A, B), whereA andB are measurable functions from a compact intervalI to Ropfn,n and Ropfn,m, respectively, andA is Lebesgue integrable. Also, let this space be endowed with the topology of theL1-norm with respect toA and the topology of convergence in measure with respect toB. Then, the set of all pairs (A, B), for which the corresponding linear control system

$$(S)dot x = A(t)x + B(t)u(t),a.e.t in I,$$
Keywords:Linear control systems  complete controllability  perturbations  convergence in measure  openness  density
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