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On homogeneous polynomial approximations of nonlinear control systems

In this paper we are going to study the chain of some distributions required by nonlinear control problems associated to homogeneous polynomial nonlinear systems. The idea is due to Ruiz and Nijmeijer and basic facts are strongly inspired by their paper. The distribution studied here is the controlled invariant distribution used in the problems of local disturbance decoupling and input-output decoupling of nonlinear systems.