Abstract
Several sufficient conditions are developed for controllability of the perturbed quasi-linear system x ̇ = A(t, x, u)x + B(t, x, u)u + f(t, x, u) . In particular, these reduce to conditions on the perturbation function f which guarantee that if the linear system x ̇ = A(t)x + B(t)u is controllable, then the system x ̇ = A(t)x + B(t)u + f(t, x, u) is controllable. These conditions are growth conditions in ( x, u) and are obtained by solving a system of nonlinear integral equations.
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