A Bound on the Number of Integrators Needed to Linearize a Control System

For nonlinear control systems, we consider the problem of dynamic feedback linearization. In particular, for a restricted class of dynamic compensators that correspond to adding chains of integrators to the inputs, we give an upper bound for the order of the compensator that needs to be considered. Moreover, in the case of 2-input systems, we show that this bound is sharp. 1. Introduction The problem of dynamic state feedback linearization for nonlinear control systems arose in the late 1980s when it was realized that only a few systems are exactly, or static, state-feedback linearizable. Although partial results towards a solution to the problem of dynamically feedback linearizing a nonlinear control system have been obtained, see for example [4, 11], the complete problem is still unresolved. A particularly troubling issue is the question of whether an upper bound exists on the order of the compensator that dynamically feedback linearizes a given system. A particular class of compens..