LMI stability criterion with less variables for time-delay systems

Slack variables approach is an important technique for tackling the delay-dependent stability problem for systems with time-varying delay. In this paper, a new delay-dependent stability criterion is presented without introducing any slack variable. The technique is based on a simply integral inequality. The result is shown to be equivalent to some existing ones but includes the least number of variables. Thus, redundant selection and computation can be avoided so that the computational burden can be largely reduced. Numerical examples are given to illustrate the effectiveness of the proposed stability conditions. Recommended by Editorial Board member Young Soo Suh under the direction of Editor Jae Weon Choi. The authors would like to thank the Associate Editor and the Reviewers for their very helpful comments and suggestions. This work was supported in part by the Funds for Creative Research Groups of China under Grant 60821063, by the State Key Program of National Natural Science of China under Grant 60534010, by the Funds of National Science of China under Grant 60674021, 60774013, 60774047, National 973 Program of China under Grant No. 2009CB320604, and by the Funds of Ph.D. program of MOE, China under Grant 20060145019 and the 111 Project B08015. Xun-Lin Zhu received the B.S. degree in Applied Mathematics from Information Engineering Institute, Zhengzhou, China, in 1986, the M.S. degree in basic mathematics from Zhengzhou University, Zhengzhou, China, in 1989, and the Ph.D. degree in Control Theory and Engineer-ing from Northeastern University, Shenyang, China, in 2008. Currently, he is an Associate Professor at Zhengzhou University of Light Industry, Zhengzhou, China. His research interests include neural networks and networked control systems. Guang-Hong Yang received the B.S. and M.S. degrees in Northeast University of Technology, China, in 1983 and 1986, respectively, and the Ph.D. degree in Control Engineering from Northeastern University, China (formerly, Northeast University of Technology), in 1994. He was a Lecturer/Associate Professor with Northeastern University from 1986 to 1995. He joined the Nanyang Technological University in 1996 as a Postdoctoral Fellow. From 2001 to 2005, he was a Research Scientist/Senior Research Scientist with the National University of Singapore. He is currently a Professor at the College of Information Science and Engineering, Northeastern University. His current research interests include fault-tolerant control, fault detection and isolation, non-fragile control systems design, and robust control. Dr. Yang is an Associate Editor for the International Journal of Control, Automation, and Systems (IJCAS), and an Associate Editor of the Conference Editorial Board of the IEEE Control Systems Society. Tao Li was born in 1979. He is now pursuing a Ph.D. degree in Research Institute of Automation Southeast University, China. His current research interests include time-delay systems, neural networks, robust control, fault detection and diagnosis. Chong Lin received the B.Sci and M.Sci in Applied Mathematics from the Northeastern University, China, in 1989 and 1992, respectively, and the Ph.D in Electrical and Electronic Engineering from the Nanyang Technological University, Singapore, in 1999. He was a Research Associate with the University of Hong Kong in 1999. From 2000 to 2006, he was a Research Fellow with the National University of Singapore. He is currently a Profesor with the Institute of Complexity Science, Qingdao University, China. His current research interests are mainly in the area of systems analysis and control. Lei Guo was born in 1966. He received the Ph.D. degree in Control Engineering from Southeast University (SEU), PR China, in 1997. From 1999 to 2004, he has worked at Hong Kong University, IRCCyN (France), Glasgow University, Loughborough University and UMIST, UK. Now he is a Professor in School of Instrument Science and Opto-Electronics Engineering, Beihang University. He also holds a Visiting Professor position in the University of Manchester, UK and an invitation fellowship in Okayama University, Japan. His research interests include robust control, stochastic systems, fault detection, filter design, and nonlinear control with their applications.