Nonlinear perturbations of quasi-linear control systems

AbstractSeveral sufficient conditions are developed for controllability of the perturbed quasi-linear system ẋ = 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 ẋ = A(t)x + B(t)u is controllable, then the system ẋ = 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