Abstract
Using the differential geometric control theory, we present the necessary and sufficient conditions under which an analytic affine nonlinear system with multiple inputs is equivalent to, via state transformation without feedback, a kind of extended Brunovsky canonical form. The proof is based on a new technique for applying the Frobenius Theorem in a more convenient way by converting a set of quasilinear partial differential equations with the same main portion to a set of homogeneous linear partial differential equations.
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