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For linear control systems with coefficients determined by a dynamical
system null controllability is discussed. If uniform local null
controllability holds, and if the Lyapounov exponents of the
homogeneous equation are all non-positive, then the system is
globally null controllable for almost all paths of the dynamical
system. Even if some Lyapounov exponents are positive, an
irreducibility assumption implies that, for a dense set of paths,
the system is globally null controllable.
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