Necessary Condition and Genericity of Dynamic Feedback Linearization

A new necessary condition for dynamic feedback linearization in the sense of [3] is proposed. This condition concerns control systems x = f(x;u) with strictly less control variables than state variables. This necessary condition allows to prove the non-genericity of dynamic feedback linearizability, for the Whitney C 1 topology on mappings (x; u) ! f(x; u). However, this topology reveals to be too coarse to capture the nature of practical uncertainties: the polymerization reactor studied in [17] is shown to be linearizable via dynamic feedback for generic kinetic and thermal laws. Key words: dynamic feedback linearization, flatness, elimination theory, structural stability, chemical reactor control 1 Introduction In [18] the genericity and structural stability of affine control systems which are linearizable via dynamic feedback [3] is investigated. We address here a similar problem for general control systems where the dependence with respect to the control variables is not suppo..