Backstepping design for global robust stabilisation of switched nonlinear systems in lower triangular form

Abstract

This article deals with the global robust stabilisation for a class of switched nonlinear systems under arbitrary switchings. The system under consideration is in lower triangular form and contains uncertainty. Both common Lyapunov function and state feedback controller are simultaneously constructed by backstepping such that the closed-loop system is globally robustly asymptotically stable under arbitrary switchings. Lastly, the design method proposed is extended to the uncertain switched nonlinear systems in nested lower triangular form to solve the global robust stabilisation problem under arbitrary switchings. Two examples are given to show the effectiveness of the proposed methods.

Keywords:

• switched systems
• common Lyapunov function
• global robust stabilisation
• backstepping

Acknowledgements

The authors thank the Editor, the Associate Editor and the anonymous reviewers for their helpful comments and suggestions which have helped to improve the quality of this article. This study was supported by the National Natural Science Foundation of China under Grants 60874024 and 90816028, the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant 200801450019 and by Ministry of Education and Science of Republic Macedonia (grant 14-3154/1-17.12.2007) and by Dogus University Fund for Science.