Exponential stabilization for nonlinear systems with applications to nonholonomic systems

Abstract

The paper proposes a general framework to study the exponential stabilization problem for a wide class of nonlinear systems. By combining the concept of dilation with the method of σ-processing, a simple stability criterion is given in terms of the stability property of an augmented system. Moreover, the global ρ-exponential stability of the closed-loop system can be achieved by employing continuous controllers. A well-known nonholonomic system is given to illustrate the effectiveness of the proposed results.