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When is a time-delay system stable and stabilizable?

A time-delay system may or may not be stable for different periods of delay, and further, may or may not be stabilized via feedback. When will then a delay system be stable or unstable, and for what intervals of delay? What will be the largest range of delay that a feedback system can tolerate? Fundamental questions of this kind have long eluded engineers and mathematicians alike, yet ceaselessly invite new thoughts and solutions. In this talk I shall present an analytical tool that answers to these questions, seeking to provide exact and efficient computational solutions to stability and stabilization problems of time-delay systems, and additionally to a number of other similar control problems, which all share the same nature that the system under consideration depends on a continuously varying parameter. The approach consists of the development of eigenvalue perturbation series and intrinsic delay bounds for stabilization. The former seeks to characterize the analytical and asymptotic properties of eigenvalues of matrix functions or operators. When applied to stability problems, 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 respect to the varying 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 such systems. The latter characterizes analytically the largest range of delay for which a system can be stabilized by a feedback controller. These results depart from the currently pervasive, typically conservative LMI conditions, and yet are conceptually appealing and computationally efficient, requiring only the solution of a generalized eigenvalue problem.

Type of Seminar:
IfA Seminar
Prof. Jie Chen
Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China
Sep 24, 2012   17:15

ETZ E 8, Gloriastr. 35
Contact Person:

Prof. Roy Smith
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Biographical Sketch:
Jie Chen teaches in the field of systems and control, and signal processing. 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. From 1990 to 1993, he was with School of Aerospace Engineering and School of Electrical and Computer Engineering at Georgia Institute of Technology, Atlanta, Georgia. He joined University of California, Riverside, California in 1994, where he has been a Professor since 1999, and served as Chair for the Department of Electrical Engineering from 2001 to 2006. While on leave from University of California, he currently holds the appointment of Chair Professor of Electronic Engineering at City University of Hong Kong, Hong Kong, China. He has also held a number of guest positions and visiting appointments with institutions in Australia, China, and Japan. His main research interests are in the areas of linear multivariable systems theory, system identification, robust control, optimization, 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, and the founding Editor-in-Chief for Journal of Control Science and Engineering. He is currently an Associate Editor for Automatica.