Abstract
This note presents a set of new versions of Barbalat’s lemma combining with positive (negative) definite functions. Based on these results, a set of new formulations of Lyapunov-like lemma are established. A simple example shows the usefulness of our results.
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This work was supported by National Natural Science Foundation of China (No.60710002, 60974044) and Program for Changjiang Scholars and Innovative Research Team in University.
Mingzhe HOU received his B.E. degree in Automation in 2005 from Harbin Institute of Technology, China. Currently, he is working toward the Ph.D. degree in the Center for Control Theory and Guidance Technology at Harbin Institute of Technology. His main research interests include nonlinear control theory and guidance and control for aircrafts.
Guangren DUAN received his Ph.D. degree in Control Systems Theory in 1989 from Harbin Institute of Technology, China. From 1989 to 1991, he was a post-doctoral researcher at Harbin Institute of Technology, where he became a professor of control systems theory in 1991. Dr. Duan visited the University of Hull, UK, and the University of Sheffield, UK from December 1996 to October 1998, and worked at the Queen’s University of Belfast, UK from October 1998 to October 2002. Since August 2000, he has been elected Specially Employed Professor at Harbin Institute of Technology sponsored by the Cheung Kong Scholars Program of the Chinese government. He is currently the Director of the Center for Control Systems and Guidance Technology at Harbin Institute of Technology. His research interests include robust control, eigenstructure assignment, descriptor systems, missile autopilot design and magnetic bearing control.
Mengshu GUO received his B.S. degree from Harbin Normal University, China, in 1995 and the M.S. and Ph.D. degrees in Mathematics from Harbin Institute of Technology, Harbin, China, in 1997 and 2003, respectively. Since 2006, he has been working as an associate professor at the Department of Mathematics, Harbin Institute of Technology. His research areas include differential inclusions, optimal control and optimization.
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Hou, M., Duan, G. & Guo, M. New versions of Barbalat’s lemma with applications. J. Control Theory Appl. 8, 545–547 (2010). https://doi.org/10.1007/s11768-010-8178-z
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DOI: https://doi.org/10.1007/s11768-010-8178-z