Stochastic hybrid multi-links networks with mixed delays: stabilisation analysis via aperiodically adaptive intermittent control

ABSTRACT

This paper investigates the problem of the mean square exponential stabilisation for stochastic hybrid multi-links networks with mixed delays (SHMND) via aperiodically adaptive intermittent control. Based on a new differential inequality with mixed delays and Markovian switching, two stability criteria are derived, which weakens the restriction on parameter that determines exponential convergence rate and reduces the conservativeness. The intensity of stochastic perturbations, coupling in multi-links and intermittent control gain have a great influence on these stability criteria. Different from the previous work that studying multi-links systems, we utilise Lyapunov method and the tree-cycle identity in graph theory integrating differential inequality techniques. Furthermore, the main results are applied to the stochastic hybrid multi-links oscillators with mixed delays. Finally, we give a numerical example to illustrate the effectiveness of theoretical results.

KEYWORDS:

• Multi-links
• mixed delays
• aperiodically adaptive intermittent control
• stabilisation

Acknowledgments

The authors really appreciate the valuable comments of the editors and reviewers. This work was supported by Shandong Province Natural Science Foundation (Nos. ZR2018MA005, ZR2018MA020, ZR2017MA008); the Key Project of Science and Technology ofWeihai (No. 2014DXGJMS08) and the Innovation Technology Funding Project in Harbin Institute of Technology (No. HIT.NSRIF.201703).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Shandong Province Natural Science Foundation (Nos. ZR2018MA005, ZR2018MA020, ZR2017MA008); the Key Project of Science and Technology of Weihai (No. 2014DXGJMS08) and the Innovation Technology Funding Project in Harbin Institute of Technology (No. HIT.NSRIF.201703).

Notes on contributors

Sen Li

Sen Li was born in 1993. She is currently a doctoral student in Harbin Institute of Technology, China. Her current research interests include stability theory for stochastic differential equations.

Huadong Sun

Huadong Sun was born in 1999. He is currently an undergraduate student in the Department of Mathematics, Harbin Institute of Technology, China. He current research interests include stability of coupled systems.

Wenxue Li

Wenxue Li was born in 1981. He received his Ph.D. degree from Harbin Institute of Technology, China, in 2009. He is currently an associate professor in Harbin Institute of Technology at Weihai. His current research interests include stability theory for stochastic differential and integral equations.