A reliable graphical criterion for TDS stability analysis

Abstract

The paper considers the stability issue of linear systems with commensurate delays. This issue can be well characterised by the distribution of roots of system's characteristic equation. At first, distribution boundary of the roots (with positive real parts) is explicit given in a practical way. Subsequently, a reliable graphical stability criterion for calculating the number of unstable roots is deduced, associating with auxiliary polynomial which plays an important role in the analysis of high order and complex systems. Moreover, a procedure for drawing the winding curve of characteristic function in finite path is proposed. At last, typical examples are given to illustrate that the result carried out is reliable and efficient.

Keywords:

• Time delay system
• argument principle
• graphical criterion

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by National Natural Science Foundation of China (NNSF) [grant numbers 61603121 and 61673160].

Notes on contributors

Tiao Yang Cai

Tiao-Yang Cai received the B. S. degree in computer science and technology from Hebei University of Engineering, Handan, China, in 2002, the M. S. and Ph.D. degrees from Hebei Polytechnic University and Northeastern University, in control theory and control engineering in 2009 and 2014, respectively. He is currently an associate professor in the College of Engineering, Hebei Normal University, Shijiazhuang. His research interests cover the time delay systems, neural networks and networked control systems.

Hui Long Jin

Hui-Long Jin obtained the B. S. degree in communication engineering from Hebei Normal University, Shijiazhuang, in 1993. He received his M.S. and Ph.D. degrees in circuits and systems from the Yanshan University in 2003 and 2012 respectively. He is currently a professor at the College of Engineering, Hebei Normal University. Jin’s research interests are pattern recognition and signal processing.

Xiang Peng Xie

Xiang-Peng Xie received the B.S. degree and Ph.D. degree in engineering from Northeastern University, Shenyang, China, in 2004 and 2010, respectively. From 2012 to 2014, he was a Postdoctoral Fellow with the Department of Control Science and Engineering, Huazhong University of Science and Technology. He is currently an Associate Professor with the Institute of Advanced Technology, Nanjing University of Posts and Telecommunications, Nanjing, China. His research interests include fuzzy modeling and control synthesis, state estimations, optimization in process industries and intelligent optimization algorithms.