Globally uniformly asymptotical stabilisation of time-delay nonlinear systems

Abstract

Globally uniformly asymptotical stabilisation of nonlinear systems in feedback form with a delay arbitrarily large in the input is dealt with based on the backstepping approach in this article. The design strategy depends on the construction of a Lyapunov–Krasovskii functional. A continuously differentiable control law is obtained to globally uniformly asymptotically stabilise the closed-loop system. The simulation shows the effectiveness of the method.

Keywords:

• backstepping
• stabilisation
• nonlinear systems
• time-delay
• Lyapunov–Krasovskii functionals

Acknowledgements

The authors would like to thank the Associate Editor and the anonymous reviewers for their many helpful suggestions. The authors are grateful for the support of the National Natural Science Foundation of China (Grant No. 60774011, No. 60674024). This work is partially supported by the National Natural Science Foundation of China (No. 60774011, No. 60674024) and the Natural Science Foundation of Fujian Province in China (No. 2008J0026).