Linearization by Prolongations: New Bounds on the Number of Integrators

This paper gives a bound on the number of integrators needed to linearize a control system with an arbitrary number of inputs. Although some work has been done in this direction, our bound improves the existing results for systems with four or more inputs. The bound for two input systems is the same as the one that appeared in the literature. The bound for three input systems has been improved further in a previous paper.