Stability of nonlinear stochastic Markov jump system with mode-dependent delays and applications

ABSTRACT

The pth moment stability of stochastic Markov jump systems (SMJSs) with time-delays and polynomial growth was investigated in this paper. Both the involved time-delays and polynomial growth are mode dependent. By using the new property of the polynomial as well as the relation between the time-delay and the generator of the Markov-chain, sufficient pth moment stability criteria are proposed. Meanwhile, the robustness of the stable SMJSs is also considered, which reveals that how much perturbation the stable SMJSs can tolerate. As an application, the consensus of stochastic multi-agent systems with nonlinear dynamics is investigated. Finally, the effectiveness of our results is illustrated by examples.

Keywords:

• Nonlinear stochastic systems
• mode-dependent delays
• stability
• consensus

2010 Mathematics Subject Classification:

• 93e03

Acknowledgments

The authors would like to thank the referees for their detailed comments and helpful suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61803098]; Innovative Research Team Program of Guangdong Province Science Foundation [grant number 2018B030312006] and the Local Innovative and Research Teams Project of Guangdong Special Support Program [grant number 2019BT02X353].