Abstract
In this paper, a sufficient linear matrix inequality (LMI) condition is presented for robust stability analysis of continuous-time linear time-invariant (LTI) systems in polytopic domains. The underlying idea behind the proposed approach is to introduce a family of complex functions which map the closed right-hand side of the complex plane into the inside of the closed unit circle centered at the origin. Then, the mapping properties are used to assure that all the eigenvalues of a system are located in the open left-hand side of the complex plane. Examples show the validity of the proposed condition.
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Recommended by Editorial Board member Tae-Hyoung Kim under the direction of Editor Myotaeg Lim.
This work was supported by the Human Resources Development program (No. 20124010203240) of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Knowledge Economy and by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No.: 2013030457).
Dong Hwan Lee received his B.S. degree in Electronic Engineering from Konkuk University, Seoul, Korea and his M.S. degree in Electrical and Electronic Engineering from Yonsei University, Seoul, Korea, in 2008 and 2010, respectively. His current research interests include stability analysis in fuzzy systems, fuzzy-model-based control, and robust control of uncertain linear systems.
Myung Hwan Tak received his B.S. and M.S. degrees from the School of Electronics and Information Engineering at Kunsan National University, Kunsan, Korea, in 2009 and 2011, respectively. He is currently working toward a Ph.D. degree at the School of Electronics and Information Engineering at Kunsan National University, Kunsan, Korea. His research interests include intelligent robot, swarm robot, robot vision, and human-robot interaction.
Young Hoon Joo received his B.S., M.S., and Ph.D. degrees in Electrical Engineering from Yonsei University, Seoul, Korea, in 1982, 1984, and 1995, respectively. He worked with Samsung Electronics Company, Seoul, Korea, from 1986 to 1995, as a project manager. He was with the University of Houston, Houston, TX, from 1998 to 1999, as a visiting professor in the Department of Electrical and Computer Engineering. He is currently a professor in the Department of Control and Robotics Engineering, Kunsan National University, Korea. His major interest is mainly in the field of intelligent robot, intelligent control, human-robot interaction, and intelligent surveillance systems. He served as President for Korea Institute of Intelligent Systems (KIIS) (2008–2009) and is serving as Editor for the Intelligent Journal of Control, Automation, and Systems (IJCAS) (2008-present) and is serving as the Vice-President for the Korean Institute of Electrical Engineers (KIEE) (2013-present).
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Lee, D.H., Tak, M.H. & Joo, Y.H. A Lyapunov functional approach to robust stability analysis of continuous-time uncertain linear systems in polytopic domains. Int. J. Control Autom. Syst. 11, 460–469 (2013). https://doi.org/10.1007/s12555-012-0426-1
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DOI: https://doi.org/10.1007/s12555-012-0426-1