Time-varying exponential stabilization of chained form systems based on a backstepping technique

It is known that the kinematic model of several nonholonomic systems can be converted into a chained form control system. Asymptotic stabilization of any equilibrium point of this system cannot be achieved by means of a continuous pure state feedback but can be obtained by using a time-varying continuous feedback. In the present paper, a backstepping technique is used to derive explicit continuous time-varying feedbacks that ensure exponential stability of the closed-loop system. Like in other recent studies on the same topic, exponential convergence is obtained by using the properties associated with homogeneous systems. A complementary and novel feature of the proposed control design technique lies in the estimation of a lower bound of the asymptotic rate of convergence as a function of a reduced set of control parameters which is independent of the system's dimension.