Input-output linearization with state equivalence and decoupling

The authors attempt to characterize the whole class of nonlinear systems that can be linearized to controllable and decouplable linear systems. The authors present the necessary and sufficient conditions for their problem to be solvable. More importantly, they explicitly characterize the nonlinear system satisfying these conditions by a set of parameters which are invariant under the group action of state feedback and transformation. This set of parameters can be calculated without solving a set of partial differential equations. Using this set of parameters, one can directly determine which of the canonical forms of decouplable and controllable linear systems is feedback equivalent to the nonlinear system. For the design of decoupled systems with linear input-output dynamic characteristics, it is more convenient to deal with the canonical form which is the simplest representation of the original system