Polynomial approach to nonlinear-system control via the exact state-input linearization method

Linearization by feedback, whether in the dynamic meaning of input-output or the dynamic sense of the state-input, is a very important strategy for the design of non-linear system regulators. In addition, a control via Exact State Input Linearization requires rigorous conditions as well as the determination of a suitable diffeomorphism. In fact, the main objective of this paper is the analysis and resolution of the difficulties of the Exact State Input Linearization formalism by developing an analytical approach which my lead to the pratical implementation of this formalism. Thus, the stability region is studied so as to determine the stability of such a system. These two studies will be applied to a preliminary example.