Finite-time boundedness of state estimation for semi-Markovian jump systems with distributed leakage delay and linear fractional uncertainties

ABSTRACT

In this paper, the problem of finite-time bounded control for uncertain semi-Markovian jump neural networks with mixed delays which include distributed leakage delay (DLD) and mixed time-varying delays is considered. The system not only contains semi-Markovian jump, linear fractional uncertainties (LFUs), mixed time-varying delays but also includes distributed time delays in the leakage term which is not yet investigated in existing papers. Firstly, uncertainty parameters in the systems are solved by LFU based on the new model. Secondly, a novel augmented Lyapunov–Krasovskii functional (LKF) which involves more information about time-varying delays is constructed. Moreover, latest integral inequalities and time-delays division method are used to estimate the derivative of proposed LKFs. Thirdly, in the framework of uncertainty, semi-Markovian jump, DLD, mixed delays and external disturbance, a full-order state estimator is constructed such that the error dynamic system is finite-time bounded under the condition of given linear matrix inequalities. Finally, usefulness and advantages of the obtained results are verified by three numerical examples.

KEYWORDS:

• Semi-Markovian jump neural networks (S-MJNNs)
• distributed leakage delay (DLD)
• linear fractional uncertainties (LFUs)
• delay division
• finite-time boundedness

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was financially supported by the National Natural Science Foundation of China [grant number 61771004].

Notes on contributors

Yaonan Shan

Yaonan Shan was born in Anyang, China. She received B.S. degree from Zhongyuan University of Technology, Zhengzhou, China, in 2015. Now she is working towards the Ph.D. degree in School of Information and Software Engineering at the University of Electronic Science and Technology of China. Her current research interests including stability theorem, the robustness stability, time-delay system and neural networks.

Kun She

Kun She received the Ph.D. degree in computer application from University of Electronic Science and Technology of China. He is currently a Professor of the School of Information and Software Engineering at University of Electronic Science and Technology of China. His research works focus on network safety, cloud computing and so on, and more than 100 scholar papers were published in these years.

Shouming Zhong

Shouming Zhong graduated from University of Electronic Science and Technology of China, majoring applied mathematics on differential equation. He is a Professor of School of Mathematical Sciences, University of Electronic Science and Technology of China, on June 1997-present. He is a Director of Chinese Mathematical Biology Society, the Chair of Biomathematics in Sichuan, Editors of Journal of Biomathematics. He has reviewed for many journals, such as Journal of Theory and Application on Control, Journal of Automation, Journal of Electronics and Journal of Electronics Science. His research interest is stability theorem and its application research of the differential system, the robustness control, neural network and biomathematics.

Jun Cheng

Jun Cheng received the B.S. degree in mathematics and applied mathematics from Hubei University for Nationalities, Enshi, China, in 2010, and the Ph.D. degree in instrumentation science and technology from the University of Electronic Science and Technology of China, Chengdu, China, in 2015. He is currently with College of Mathematics and Statistics, Guangxi Normal University, and also a Postdoctoral Researcher with the School Mathematical Sciences, University of Electronic Science and Technology of China. From September 2013 to September 2014, he was a visiting Scholar with the Department of Electrical and Computer Engineering, National University of Singapore, Singapore. He was a visiting Scholar with the Department of Electrical Engineering, Yeungnam University, Gyeongsan, South Korea, from May 2016 to June 2016. His current research interests include analysis and synthesis for stochastic hybrid systems, networked control systems, robust control and nonlinear systems.

Can Zhao

Can Zhao was born in Fuyang, China. He received B.S. degree from Fuyang Normal University, Fuyang, China, in 2015. Now he is working towards the Ph.D. degree in School of Mathematics Sciences at the University of Electronic Science and Technology of China. His current research interests including stability theorem, nonlinear control, neural networks and complex networks.

Qianhua Fu

Qianhua Fu received the B.S. degree in electronic information engineering from Chongqing University of Technology, China, in 2003, and received the M.S. degree in communication and information systems from University of Electronic Science and Technology of China (UESTC) in 2010. He was a R&D engineer in HUAWEI company from 2010 to 2014. He received the Ph.D. degree in communication and information systems from UESTC in 2019. He is currently working as an engineer at Xihua University. His main research interests are memristor neural network, RF circuits and systems for wireless communications and signal processing in modern communication.