A note on attraction and stability of neutral stochastic delay differential equations with Markovian switching

Abstract

This paper is concerned with neutral stochastic delay differential equations with Markovian switching (NSDDEs-MS). A kind of ψ − function is introduced and some criteria on the attractor for the product of the ψ − function are obtained. By the new criteria, the almost sure stability with the general decay rate of NSDDEs-MS could be examined, including the exponential stability and the polynomial stability. Finally, an example is provided to illustrate the applications of our results clearly.

Keywords:

• attraction
• stability
• neutral stochastic delay differential equations
• Markov chain
• generalised It formula

Acknowledgements

This work was supported by the State Key Program of National Natural Science of China under Grant No. 61134012, the National Science Foundation of China under Grant No. 11271146 and the China Postdoctoral Science Foundation funded project under Grant No. 2012M511615.

Additional information

Notes on contributors

Yinfang Song

Yinfang Song is a lecturer of the School of Information and Mathematics, Yangtze University. He received his PhD degree in the Department of Control Science and Engineering, Huazhong University of Science and Technology in 2013. His current research interests include stability of stochastic differential systems and stochastic neural networks.

Quan Yin

Quan Yin received the BS, MS degrees in industrial electrical automation, and PhD degree in Control Theory and Control Engineering from Huazhong University of Science and Technology, Wuhan, China, in 1990, 1995 and 2001, respectively. He was a postdoctoral fellow with the Huazhong University of Science and Technology from 2001 to 2003. He is currently an associate professor with the Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, China. He is the author of more than 30 research papers. His current research interests include intelligent control and embedded control systems.

Yi Shen

Yi Shen received the PhD degree from Huazhong University of Science and Technology, Wuhan, China, in 1998. He was a postdoctoral research fellow at the Huazhong University of Science and Technology during 1999–2001. He joined the Department of Control Science and Engineering, Huazhong University of Science and Technology, and became an associate professor in 2001 and was promoted to professor in 2005. From 2006 to 2007, he was a postdoctoral research fellow at the Department of Mechanical and Automation Engineering, the Chinese University of Hong Kong, Hong Kong. He has authored over 50 research papers. His main research interests lie in the fields of stochastic control and neural networks.