Abstract
This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties. A new and simple method is presented to directly decouple the Lyapunov matrix and the system dynamic matrix. Combining this method with the parameter-dependent Lyapunov function approach yields new criteria that include some existing ones as special cases. A numerical example illustrates the improvement over the existing ones.
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This work was supported in part by the Doctor Subject Foundation of China (No. 20050533015) and the National Science Foundation of China (No. 60425310, 60574014).
Xianming ZHANG was born in 1968. He received the M.S. degree in applied mathematics from Central South University, China in 1991, and he received Ph.D. degree in control theory and engineering at Central South University, China in 2006. From April 2005 to April 2006, he was a visiting scholar at Central Queensland University, Australia. Now, he is an associate professor of Central South University. His current research interests are time-delay systems, robust control and its applications.
Min WU was born in 1963. He received the B.S. and M.S. degrees in engineering from Central South University, Changsha, China in 1983 and 1986, respectively. He received a Ph.D. degree in engineering from the Tokyo Institute of Technology, Tokyo, Japan in 1999. Now, he is a professor of Central South University. He received the control engineering practice paper prize of IFAC in 1999 (jointly with M. Nakano and J. H. She). His current research interests are process control, robust control, and intelligent systems.
Jinhua SHE was born in 1963. He received the B.S. in engineering from Central South University, Changsha, China, in 1983, and an M.S. in 1990 and a Ph.D. in 1993 in engineering from the Tokyo Institute of Technology, Tokyo, Japan. In 1993, he joined the Department of Mechatronics, School of Engineering, Tokyo University of Technology; and in April, 2004 he transferred to the University’s School of Bionics, where he is currently an associate professor. He received the control engineering practice paper prize of IFAC in 1999 (jointly with M. Wu and M. Nakano). His current research interests include the application of control theory, repetitive control, expert control, Internet-based engineering education, and robotics. He is a member of the Society of Instrument and Control Engineers (SICE), the Institute of Electrical Engineers of Japan (IEEJ), and IEEE.
Dongsheng HAN was born in 1982. He received the B.S. degree in Computer Science from Shandong Normal University, China in 2004, and is currently working toward the M.S. degree in the control theory and engineering in Central Queensland University, Australia. His current research interests are Networked control and its applications.
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Zhang, X., Wu, M., She, J. et al. An improved robust stability and robust stabilization method for linear discrete-time uncertain systems. J. Control Theory Appl. 5, 99–103 (2007). https://doi.org/10.1007/s11768-004-4173-6
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DOI: https://doi.org/10.1007/s11768-004-4173-6