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If a smooth nonlinear affine control system has a controllable linear
approximation, a standard technique for constructing a smooth (linear)
asymptotically stabilizing feedbackcontrol is via the
LQR (linear, quadratic, regulator) method. The nonlinear system may
not have a controllable linear approximation, but instead may be shown
to be small (or large) time locally controllable via a high order,
homogeneous approximation. In this case one can attempt to construct
an asymptotically stabilizing...
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