Algebraic necessary and sufficient conditions of input-output linearization

This paper exposes two different versions of the input-output linearization problem by dynamic feedback for nonlinear control systems. The first one ( weak version) considers only the input-output behavior while the second one (strong version) assures linear state equations for the input-output subsy stem. It also gives the corresponding necessary and sufficient conditions f or their solvability in terms of intrinsic conditions. For the first versio n, the necessary and sufficient condition is a rank condition, which, rough ly speaking, expresses the fact that the differential output rank is equal to the rank that can be calculated when considering only the linear differe ntial relations among the output components. The condition for the second v ersion of the problem is the isomorphism of two algebraic structures constr ucted from the output components. It is shown that the structure algorithm is a convenient tool for verifying the fulfillment of these conditions, and to construct the solution when this problem is solvable. It is also establ ished that quasi-static state feedback is sufficiently general to solve the input-output linearization for classical control systems.