Sufficient conditions are derived for global and local controllability of nonlinear time-varying systems with control appearing linearly. It is shown that the controllability of x = A(t,x)x + B(t,x)u can be related to the controllability of the linear system x = A(t,z)x + B(t,z)u, where z belongs to a certain set of continuous vector functions. This result is then used to specify a class of nonlinear systems which are globally controllable.
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Davison et al. (1970) studied this question.
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