Abstract
This paper develops sufficient conditions for a general nonlinear control system ∑ 1: x ̇ = f (x, u) to be locally (resp. globally) asymptotically stabilizable via smooth state feedback. In particular, it is shown that as in the case of affine systems, this is possible if the unforced dynamic system of ∑ 1 is Lyapunov stable and appropriate controllability-like rank conditions are satisfied. Our results incorporate a series of well-known stabilization theorems proposed in the literature for affine control systems and extend them to nonaffine nonlinear control systems.
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