The dynamics of non holonomic mechanical system are described by the classical Euler-Lagrange equations subjected to a set of non-integrable constraints. Non holonomic systems are strongly accessible whatever the structure of the constraints. They cannot be asymptotically stabilized by a smooth pure state feedback. However smooth state feedback control laws can be designed which guarantee the global marginal stability of non holonomic systems.
Campion, G., Dandreanovel, B., & Bastin, G. (1991). Controllability and State Feedback Stabilizability of Nonholonomic Mechanical Systems. Lecture Notes in Control and Information Sciences, 162, 106-124. https://doi.org/10.1007/BFb0039268 (Original work published 1991)