this paper, we restrict our attention to smooth timevarying control of nonholonomic systems. We show for the first time that smooth aperiodic time-varying controls for exponentially stabilizing a nonholonomic system can be easily synthesized if the system is augmented with some auxiliary state(s). By comparison with other existing (continuous and discontinuous) time-varying control results, besides the simplicity of the design procedure, the trajectory of system states designed by our control strategy avoids the zig-zag path and is thus more reasonable, and the convergence exponents can be evaluated easily and assigned arbitrarily. The method also overcomes the drawback of discontinuity of the existing pure-state feedback approaches. The proposed method proves to be effective for a wide class of nonholonomic systems including the chained form system, multiple chained form system, power form system, Brockett system, etc. Simulation examples are introduced to demonstrate the effectiveness of the method.