6.2 Dynamic System Linearization using Non-Linear Feedback
The linearity of the control system using non-linear feedback requires the accessibility to all state variables. It is assumed that all necessary variables are measured and directly calculated or estimated using a model or observer system.
The linearization process of non-linear systems is widely discussed in [2,3,8,26,27]. To use non-linear feedback, it is desirable to obtain a mathematical description of the non-linear dynamic system as a system of differential equations. It is assumed that the dynamic system is described by equations [2,3,8,19]:
are vector functions.
Methods of differential geometry  make it possible to convert the above-described system by using a non-linear change of variables and non-linear feedback to the next form:
where A and B are constant matrices, so that a pair (A, B) is controllable.
Linearization of the system using variables transformation and non-linear feedback may be realized, as in  The first step of linearization is to choose new variables:
such that the differential ...