On finite-time stability of nonautonomous nonlinear systems

ABSTRACT

This paper is concerned with the finite-time stability (FTS) of nonautonomous nonlinear systems. Firstly, a new definition of FTS for nonautonomous nonlinear systems is introduced. Then some sufficient conditions on FTS for nonautonomous nonlinear systems are established based on Lyapunov function. Furthermore, the conditions are shown to be necessary and sufficient for linear time-varying systems. Finally, several numerical examples are given to illustrate our results.

KEYWORDS:

• Finite-time stability
• nonautonomous systems
• nonlinear systems
• Lyapunov function
• time-varying systems

Acknowledgments

The authors would like to thank the editor and the reviewers for their constructive comments and suggestions which improved the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Junhui Zhang  http://orcid.org/0000-0001-6879-5418

Qing-Guo WANG  http://orcid.org/0000-0002-3672-3716

Jitao Sun  http://orcid.org/0000-0002-9581-8336

Additional information

Funding

This work is supported by the NNSF of China under grant 61673296. Qing-Guo WANG acknowledges the financial support of the National Research Foundation of South Africa (Grant Number: 113340) and Oppenheimer Memorial Trust grant, which partially funded his research on this work.