EXPONENTIAL STABILIZATION OF NONHOLONOMIC CHAINED SYSTEMS

This paper presents a feedback control scheme for the stabilization of two-input, driftless, chained nonholonomic systems, also called chain ed form. These systems are controllable but not asymptotically stabili zable by a smooth static-state feedback control law. In addition, expo nential stability cannot be obtained with a smooth, time-varying feedb ack control law, Here, global, asymptotical stability with exponential convergence is achieved about any desired configuration by using a no nsmooth, time-varying feedback control law. The control law depends, i n addition to the state and time, on a function which is constant exce pt at predefined instants of time where the function is recomputed as a nonsmooth function of the state. The inputs are differentiable with respect to time and tend exponentially toward zero. For use in the ana lysis, a lemma on the exponential convergence of a stable time-varying nonlinear system perturbed by an exponentially decaying signal is pre sented. Simulation results are also shown.