Extended Quadratic Controller Normal Form and Dynamic State Feedback Linearization of Nonlinear Systems

In this paper, a set of extended quadratic controller normal forms of linearly controllable nonlinear systems is given, which is the generalization of the Brunovsky form of linear systems. A set of invariants under the quadratic changes of coordinates and feedbacks is found. It is then proved that any linearly controllable nonlinear system is linearizable to second degree by a dynamic state feedback.