Abstract: A time-delay system may or may not be stable for different lengths of delay, and further, may or may not be stabilized via feedback. When will then a delay system be stable or unstable? When can an unstable delay system be stabilized? What range of delay can a feedback system tolerate to maintain stability? Fundamental questions of this kind have long eluded engineers and mathematicians alike, yet ceaselessly invite new thoughts and solutions. In this talk sequence we present a systematic analysis of the stability and stabilization of time-delay systems, wherein we attempt to provide tools and techniques that answer to the questions alluded to above, seeking to provide exact and efficient computational solutions to stability and stabilization problems of time-delay systems. We develop in full an operator-theoretic approach that departs from the currently pervasive LMI solution approaches, notable for both its conceptual appeal and its computational efficiency. Extensions to networked control systems and multi-agent systems will also be discussed. 

The stability analysis approach in question will be preceded by the development of eigenvalue perturbation series, which characterize the analytical and asymptotic properties of eigenvalues of matrix functions or operators. When applied to stability problems of delay systems, the essential issue dwells on the asymptotic behavior of the critical eigenvalues on the imaginary axis, that is, on how the imaginary eigenvalues may vary with the delay parameter. This behavior determines whether the imaginary eigenvalues cross from one half plane into another, and hence plays a critical role in determining the stability of delay systems. The approach requires solving only a generalized eigenvalue problem, thus lending a truly efficient solution to high-dimensional systems with many delays. For stabilization of delay systems, we focus on the fundamental delay "justify"> 

Biosketch 

Jie Chen is a Chair Professor in the Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China. He received the B.S. degree in aerospace engineering from Northwestern Polytechnic University, Xian, China in 1982, the M.S.E. degree in electrical engineering, the M.A. degree in mathematics, and the Ph.D. degree in electrical engineering, all from The University of Michigan, Ann Arbor, Michigan, in 1985, 1987, and 1990, respectively. 

Prior to joining City University, he was with School of Aerospace Engineering and School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia from 1990 to 1993, and with University of California, Riverside, California from 1994 to 2014, where he was a Professor and served as Professor and Chair for the Department of Electrical Engineering from 2001 to 2006. His main research interests are in the areas of linear multivariable systems theory, system identification, robust control, optimization, time-delay systems, networked control, and multi-agent systems.  He is the author of two books, respectively, (with G. Gu) Control-Oriented System Identification: An H-infinity Approach (Wiley-Interscience, 2000), and (with K. Gu and V.L. Kharitonov) Stability of Time-Delay Systems (Birkhauser, 2003). 

An elected Fellow of IEEE, Fellow of AAAS, Fellow of IFAC and a Yangtze Scholar/Chair Professor of China, Dr. Chen was a recipient of 1996 US National Science Foundation CAREER Award, 2004 SICE International Award, and 2006 Natural Science Foundation of China Outstanding Overseas Young Scholar Award. He served on a number of journal editorial boards, as an Associate Editor and a Guest Editor for the IEEE Transactions on Automatic Control, a Guest Editor for IEEE Control Systems Magazine, an Associate Editor for Automatica, and the founding Editor-in-Chief for Journal of Control Science and Engineering. He is currently an IEEE Control Systems Society (CSS) Distinguished Lecturer and serves as an Associate Editor for SIAM Journal on Control and Optimization. He was a member on IEEE CSS Board of Governors in 2014 and has served as IEEE CSS Chapter Activities Chair since 2015. 

Tian Qi was born in Chaoyang, Liaoning Province, China in 1981. She received the B.S. degree in automation from Hangzhou Dianzi University, Hangzhou, China in 2003, the M.S. degree and the Ph.D. degree in control theory and control engineering, from South China University of Technology, Guangzhou, China in 2006 and 2009, respectively. 

Dr. Tian Qi joined the South China University of Technology in 2009, where she is currently a Lecturer. From May 2011 to August 2011, she was with the Department of Electronic Engineering, City University of Hong Kong, as a postdoctoral researcher. From January 2012 to December 2012, she was a Research Associate in the Department of Electrical and Computer Engineering, Hong Kong University of Science and Technology. Her main research interests are in the areas of networked control, multi-agent systems, time-delay systems, robust control and optimization.