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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.