Abstract
A system is totallyG-controllable if every pointx0 of the state spaceEn can be steered to the targetG in finite time and can be held inG forever afterward. Sufficient conditions are developed for the totalG-controllability of the linear system $$\dot x(t) = A(t)x(t) + B(t)u(t)$$ (a) and its perturbation $$\dot x(t) = A(t)x(t) + B(t)u(t) + F(t,x(t),u(t)),$$ (b) where the targetG is an affine manifold inEn. We state conditions on the perturbation functionF which guarantee that, if (a) is totallyG-controllable, then so is (b). These conditions onF are natural and are obtained by solving a system of nonlinear integral equations by the Leray-Schauder fixed-point theorem.
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