Linearization by Redundancy and Stabilization of Nonlinear Dynamical Systems: A State Transformation Approach

This paper presents a new concept of linearization of nonlinear dynamical systems. The used approach relies on immersion and static state feedback transformations. As a first contribution, we show how we can make the transformed immersed system dynamics available for control. Therefore, the vector of control in the immersed system dynamics is now getting out of any premultiplying column matrix. The main stream of our approach is that the immersed system dynamics is regarded as the nonreduced-order dynamics of a mechanical constrained system that can be expressed in terms of an unconstrained (or initial) dynamics and a term of constraint. Further, a systematic way of expressing the immersed dynamics in terms of an initial dynamics and a term of constraint is discussed. At this point, our linearization approach consists of designing an immersion and a static state feedback which render the initial dynamics linear, however, the whole transformed immersed system dynamics is still nonlinear. In order to demonstrate the effectiveness of the presented linearization approach, we show that the stabilization problem for the original nonlinear system dynamics is reduced to a stabilization problem for a linear system dynamics that represents the initial dynamics of the transformed immersed system dynamics. We believe that our linearization approach may be very useful for the global output feedback tracking control problem of nonlinear systems