Two novel stability criteria for linear systems with interval time-varying delays

Abstract

This paper analyses the stability problem of linear systems with interval time-varying delay. In regard to the delay, it has the lower and upper bounds and its derivative is unknown or itself is not differentiable. First of all, it is the first time that the delay-related triple integral terms are used to construct the augmented Lyapunov–Krasovskii functional (LKF) and the delay-related integral quadratic terms are estimated by the third-order free-matrix-based integral inequalities (TFIIs). Then, based on the same LKF and same TFIIs and by introducing two sets of state vectors, the derivative of the LKF is presented as the quadratic and quintic polynomials about the delay respectively. Next, for the quadratic and quintic polynomials, new negative definite conditions (NDCs) are provided to form the linear matrix inequality (LMI) conditions. Finally, the advantages of these two criteria are checked through some classical numerical examples.

Keywords:

• Delayed systems
• interval time-varying delay
• triple integral terms
• quadratic and quintic polynomials
• negative definite conditions

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

The data and materials that support the results or analyses presented in this paper are freely available from the corresponding author upon request.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant numbers 62073143, 61922063, 62103146], Program of Shanghai Academic Research Leader [grant number 19XD1421000], Shanghai and HongKong-Macao-Taiwan Science and Technology Cooperation Project [grant number 19510760200], Shanghai Shuguang Project [grant number 18SG18], Innovation Program of Shanghai Municipal Education Commission [grant number 2021-01-07-00-02-E00107], and Project funded by China Postdoctoral Science Foundation [grant numbers 2020TQ0096, 2021M690056].

Notes on contributors

Zhengliang Zhai

Zhengliang Zhai received the M.Sc. degree in electrical engineering from the Hunan University of Technology, Zhuzhou, China, in 2020. He is currently pursuing the Ph.D. degree with the School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang, China. His current research interests include time delay systems, networked control systems and multi-agent systems.

Huaicheng Yan

Huaicheng Yan received his BSc degree in automatic control from Wuhan University of Technology, China, in 2001, and the PhD degree in control theory and control engineering from Huazhong University of Science and Technology, China, in 2007. In 2011, he was a Research Fellow with the University of Hong Kong, Hong Kong, for three months, and also a Research Fellow with the City University of Hong Kong, Hong Kong, in 2012, for six months. Currently, he is a Professor with the School of Information Science and Engineering, East China University of Science and Technology, Shanghai,China. He is an associate editor for IEEE Transactions on Neural Networks and Learning Systems, International Journal of Robotics and Automation and IEEE Open Journal of Circuits and Systems. His research interests include networked control systems, multi-agent systems and robotics.

Shiming Chen

Shiming Chen received the B.Sc. degree in automation and the Ph.D. degree in control theory and control engineering from the Huazhong University of Science and Technology, Wuhan, China, in 1998 and 2006, respectively. He is currently a Professor with the School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang, China. His current research interests include swarm dynamics and cooperative control, and complex network.

Yongxiao Tian

Yongxiao Tian received the M.S. degree in mathematics from Zhejiang Normal University, Zhejiang, China, in 2016, and the Ph.D. degree in control science and engineering form East China University of Science and Technology, Shanghai, China in 2021. He is now a Postdoctoral Fellow with the School of Information Science and Engineering, East China University of Science and Technology, Shanghai, China. His current research interests include stochastic systems and networked control systems.

Jing Zhou

Jing Zhou received the B. E. degree from Wuhan University of Technology in school of mechanical and electronic engineering in 2002, the M.E. degree in pattern recognition and intelligent systems in 2005 and Ph.D. degree in control science and engineering in 2009 from Huazhong University of Science and Technology, Wuhan China. Her current research interests include artificial intelligent and object detection.