Nonsingular covering of nonlinear control systems and its application to feedback linearization along a reference trajectory

A quasi-coordinate system is introduced to analyze the behavior of a nonlinear control system in the neighborhood of a singular point. The quasi-coordinate is defined on open sets which are called nonsingular covers since, under the quasi-coordinate, the distribution can be expressed by the nonsingular quasi-distributions. A feedback linearization along a reference trajectory is analyzed for an application of the nonsingular covers and the index invariance of the linear approximation system is interpreted as a geometric property such that the reference trajectory is included in the nonsingular region. Finally, the algorithm to get an exact linearization along the reference trajectory by the state feedback and the transformation of the quasi-coordinate is presented