  In the article the problem of output setpoint tracking for affine non-linear
system is considered. Presented approach combines state feedback linearization
and homotopy numerical continuation in subspaces of phase space where feedback
linearization fails. The method of numerical parameter continuation for solving
systems of nonlinear equations is generalized to control affine non-linear
dynamical systems. The illustrative example of control of MIMO system which is
not static feedback linearizable is given. Application of proposed method
demonstrated on the speed and rotor magnetic flux control in the three-phase
asynchronous motor.

Systems and Control