Time-varying control of a class of nonholonomic systems

In this paper we propose a general dynamic model for describing a class of nonholonomic systems including extended chained systems, extended power systems, underactuated surface vessel systems etc. We prove that by introducing an assistant state variable(s), this class of nonholonomic systems can be transformed into linear time-varying control systems, and the asymptotic exponential stability is thus achieved by using a smooth time-varying feedback control law.