Parameter homotopy continuation for feedback linearization of non-regular control-affine nonlinear systems

In this article feedback linearization for control-affine nonlinear systems is extended to systems where linearization is not feasible in the complete state space by combining state feedback linearization and homotopy numerical continuation in subspaces of the phase space where feedback linearization fails. Starting from the conceptual simplicity of feedback linearization, this new method expands the scope of their applicability to irregular systems with poorly expressed relative degree. The method is illustrated on a simple SISO–system and by controlling the speed and the rotor flux linkage in a three phase induction machine