Necessary conditions of exponential stability for a class of linear neutral-type time-delay systems

ABSTRACT

For a class of linear neutral-type time-delay systems (NTTDSs), this paper will present necessary exponential stability conditions by employing the Lyapunov--Krasovskii functional approach. Since these conditions are represented by the Lyapunov matrix and the neutral coefficient matrix, they not only offer a novel tool for analysing stability of linear NTTDSs by characterising instability domains, but also extend the existing results of the neutral-delay-free systems. As a medium step, the relations between the Lyapunov matrix and the fundamental matrix are characterised. The validation of the obtained results is explained by numerical examples and comparison with some existing results.

KEYWORDS:

• Exponential stability
• neutral-type time-delay systems
• complete-type Lyapunov–Krasovskii functional

Acknowledgments

The authors thank the anonymous referees for their helpful comments and suggestions, which greatly improved this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [11371006, 61773131, U1509217]; Australian Research Council [DP170102644]; 111 Project [B17048]; the Heilongjiang University Specialized Fund for the Basic Research Operating Expenses Program of Colleges and Universities in Heilongjiang Province [HDJCCX-2016212]; and the Heilongjiang University Innovation Fund for Graduates [YJSCX2017-064HLJU].