Controllability of nonlinear systems to affine manifolds (Q1117174)

Controllability to an affine manifold involves controlling a system to a target defined by the generalized boundary condition \(\Gamma x=r\), where \(\Gamma\) : \(C^ n\to R^ n\) is a bounded linear operator on the continuous functions, as defined for ordinary differential equations by \textit{A. G. Kartsatos} [Indiana Univ. Math. J. 23, 1021-1029 (1974; Zbl 0303.34014)]. In this paper, sufficient conditions are obtained for such controllability for linear systems and for a class of nonlinear perturbations of linear systems.