Global output feedback stabilisation of high-order nonlinear systems with multiple time-varying delays

Abstract

This paper investigates the problem of global output feedback stabilisation for a class of high-order nonlinear systems with multiple time-varying delays. By using backstepping recursive technique and the homogeneous domination approach, a continuous output feedback controller is successfully designed, and the global asymptotic stability of the resulting closed-loop system is proven with the help of an appropriate Lyapunov– Krasovskii functional. Two simulation examples are given to illustrate the effectiveness of the proposed approach.

Keywords:

• high-order nonlinear systems
• multiple time-varying delays
• output-feedback
• homogeneous domination approach
• global asymptotic stability

Acknowledgements

The authors thank the editor and the anonymous reviewers for their constructive comments and suggestions for improving the quality of the paper.

Additional information

Funding

This work has been supported in part by National Nature Science Foundation of China [grant number 61403003], [grant number 61073065], [grant number 61273091]; the Key Program of Science Technology Research of Education Department of Henan Province [grant number 13A120016], [grant number 14A520003].