Dynamic feedback linearization

Abstract

It is shown how a generalization of E. Cartan's results (1908, 1914) on absolute equivalence of differential systems provides necessary and sufficient conditions for local dynamic feedback linearization of control systems. The authors prove that the only extended systems which should ever be considered are those obtained by partial prolongation. The problem of dynamic feedback linearizability of a system with p controls is essentially the problem of characterizing the absolute equivalence class of the contact system. It is shown that the problem of absolute equivalence and hence of linearizability may always be reduced to a problem of G-structures after taking partial prolongations of the original system. The approach used first 'sorts' systems with a diffeomorphism group which properly contains the dynamic feedback transformations. If a system is not linearizable by the larger transformation group, then it is not linearizable by a subgroup. If it proves linearizable by the larger group, then the analysis must be refined to show that the subgroup is sufficient. A brief description of the notion of absolute equivalence and a characterization of the absolute equivalence class of the contact system are given.<>