Global uniform asymptotical stability of a class of nonlinear cascaded systems with application to a nonholonomic wheeled mobile robot

Abstract

In this article, we consider the stability analysis problem for a class of nonlinear cascaded systems by using homogeneous properties. Assume that the driving subsystem and the driven subsystem are both homogeneous and locally uniformly asymptotically stable. If the cascaded term satisfies a given inequality, then the cascaded system is globally uniformly asymptotically stable. Furthermore, in the case that both degrees of homogeneity are negative, the cascaded system is globally uniformly finite-time stable. Compared with the existing methods, the conditions given in this article are much easier to verify. These stability results are applied to the global tracking control problem of a nonholonomic wheeled mobile robot. Simulation results are provided to show the effectiveness of the methods.

Keywords:

• cascaded system
• homogeneous system
• asymptotical stability
• finite-time stability
• wheeled mobile robot
• tracking control

Acknowledgements

This work was supported by the Natural Science Foundation of China (60504007, 61074013), the Specialized Research Fund for the Doctoral Programme of Higher Education of China (20090092110022), the Graduate Innovation Programme of Jiangsu Province and the Scientific Research Foundation of the Graduate School of Southeast University.