Partial Stabilizability of Nonholonomic Systems

This paper addresses the concept of partial stabilization for driftless control systems called ”nonholonomic systems”. We introduce a class of feedback transformations that transforms our system in to a multi-chained triangular form. We show that we can bounded the first component; this can be done by using a smooth feedback control depending on the state. In addition the (n − 1) other components will be stabilized asymptotically. In first step this approach is applied to unicycle system and in second step it is generalized to nonholonomic systems with m controls . Key-Words: Brockett condition; Partial stabilization; Systems without drift; Barbashin-Krasovski theorem.