Dimensions of linear subsystems of nonlinear systems

An open problem for nonlinear systems with outputs is to find the largest dimension of an input-output linearized subsystem achievable by feedback and coordinate change. Previous results are known for single input, single output (SISO) systems and for multi-input, multi-output (MIMO) systems there a feedback is given and a coordinate change must be found. In this paper, the authors offer a solution to this problem for general MIMO nonlinear systems and developed a systematic method to compute the desired feedback and coordinate change.