Algebraic necessary and sufficient conditions of input-output linearization (Q2716421)

Two different versions of the problem of input-output linearization by dynamic feedback for nonlinear control systems are investigated. 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 subsystems. One gives the corresponding necessary and sufficient conditions for their solvabilty in terms of intrinsic conditions. For the first version, the necessary and sufficient condition is a rank condition, which, roughly speaking, expresses the fact that the differential output rank is equal to the rank that can be calculated when considering only the linear differential relations among the output components. The condition for the second version of the problem is the isomorphism of two algebraic structures constructed from the output components. The authors show 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. They also establish that quasi-static state feedback is sufficiently general to solve the input-output linearization for classical control problem.