Stochastic stability analysis for neutral-type Markov jump neural networks with additive time-varying delays via a new reciprocally convex combination inequality

ABSTRACT

This paper investigates the stochastic stability problem for a class of neutral-type Markov jump neural networks with additive time-varying delays. Firstly, to derive a tighter lower bound of the reciprocally convex quadratic terms, a new reciprocally convex combination inequality is established by using parameters transformation approach. Secondly, by fully considering the peculiarity of various time-varying delays and Markov jumping parameters, an eligible stochastic Lyapunov–Krasovskii functional is constructed. Then, by employing the new reciprocally convex combination inequality and other analytical techniques, some novel stability criteria are provided in the forms of linear matrix inequalities. Finally, four illustrated examples are given to verify the effectiveness and feasibility of the proposed methods.

KEYWORDS:

• Stochastic stability
• neutral-type Markov jump neural networks
• additive time-varying delays
• reciprocally convex combination inequality
• linear matrix inequalities

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China under grant nos. 11671206, 11601474 and 61472093, supported by the Key laboratory of numerical simulation of Sichuan Province under grant no. 2017KF002, the Graduate Research Innovation Program of Jiangsu Province under grant no.KYCX18_374 and the China Scholarship Council (CSC).

Notes on contributors

Haiyang Zhang

Haiyang Zhang received the B.Sc. from School of Information, Huaibei Normal University, Huaibei, China, in 2013 and obtained the M.Sc. from the School of Mathematics and Computer Science, Yunnan Minzu University, Yunnan, China, in 2016. Now he is working towards the Ph.D. degree in School of Science, Nanjing University of Science and Technology. His current research interests include Time-delay Systems, Stability and Control problems, Stabilisation and Synchronisation, Stochastic Jump Systems, Neural Networks, Neutral dynamical systems and Complex networks.

Zhipeng Qiu

Zhipeng Qiu received the B.Sc and M.Sc. in Applied Mathematics from Southwest Normal University, Chongqing, China, in 1996 and 1999, respectively. He received his Ph.D degree in control theory and control engineering from Nanjing University of Science and Technology, Nanjing, China, in 2003. He joined Nanjing University of Science and Technology in 1999, where he is currently a professor with the School of Science. His current research interests include mathematical modelling and analysis in ecology and epidemiology, stability theory, bifurcation theory and applications, age-structured mathematical models.

Lianglin Xiong

Lianglin Xiong received the B.Sc. in Mathematics and Applied Mathematics from Neijiang Normal University, Sichuan, China, in 2004. He received his M.Sc. and D.Sc. in Applied Mathematics from University of Electronic Science and Technology of China, Sichuan, China, in 2007 and 2009, respectively. He is on the staff of the School of Mathematics and Computer Science, Yunnan Minzu University, from March 2010 to present. In 2012, he was appointed as a professor and master tutor of Applied Mathematics. His research interests are Stability Theorem and its Application research of the Differential System, Robustness control, Neutral dynamical systems and Complex networks.

Guanghao Jiang

Guanghao Jiang received the B.Sc. and M.Sc. in Basic Mathematics from Jiangsu Normal University, Xuzhou, China, in 1996 and 2005, respectively. He received his D.Sc. in Basic Mathematics from Nanjing University, Nanjing, China, in 2008. He joined Huaibei Normal University in 2008 where he is currently a professor with the School of Mathematics. His research interests are General topology Fuzzy Mathematics and Domain theory.