Abstract
This paper gives a novel delay-dependent admissibility condition of discrete-time singular systems with time-varying delays. For convenience, the time-varying delay is assumed to be the sum of delay lower bound and the integral multiples of a constant delay. Specially, if the constant delay is of unit length, the delay is an interval-like time-varying delay. The proposed admissibility condition is presented and expressed in terms of linear matrix inequality (LMI) by Lyapunov approach. Generally, the uncertainty of time-varying delay would lead to conservatism. In this paper, this critical issue is tackled by accurately estimating the time-varying delay. Consequently, the proposed admissibility condition is less conservative than the existing results, which is demonstrated by a numerical example.
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X. Sun, Q. L. Zhang, C. Y. Yang, Z. Su, Y. Y. Shao. An improved approach to delay-dependent robust stabilization for uncertain singular time-delay systems. International Journal of Automation and Computing, vol. 7, no. 2, pp. 205–212, 2010.
X. Sun, Q. L. Zhang, C. Y. Yang, Y. Y. Shao, S. Zhan. Delay-dependent stability analysis and stabilization of discrete-time singular delay systems. Acta Automatica Sinica, vol. 36, no. 10, pp. 1477–1483, 2010. (in Chinese)
X. D. Zhao, Q. S. Zeng. H∞ output feedback control for stochastic systems with mode-dependent time-varying delays and Markovian jump parameters. International Journal of Automation and Computing, vol. 7, no. 4, pp. 447–454, 2010.
X. L. Wang, C. G. Fei, Z. Z. Han. Adaptive predictive functional control for networked control systems with random delays. International Journal of Automation and Computing, vol. 8, no. 1, pp. 62–68, 2011.
H. R. Karimi. Adaptive H∞ synchronization of master-slave systems with mixed time-varying delays and nonlinear perturbations: An LMI approach. International Journal of Automation and Computing, vol. 8, no. 4, pp. 381–390, 2011.
X. F. Jiang, Q. L. Han. Networked-induced delaydependent H∞ controller design for a class of networked control systems. Asian Journal of Control, vol. 8, no. 2, pp. 97–106, 2006.
S. Ma, Z. Cheng, C. Zhang. Delay-dependent robust stability and stabilization for uncertain discrete singular systems with time-varying delays. IET Control Theory and Applications, vol. 1, no. 4, pp. 1086–1095, 2007.
H. J. Wang, X. D. Zhao, A. K. Xue, R. Q. Lu. Delaydependent robust control for uncertain discrete singular systems with time-varying delay. Journal of Zhejiang University (Science A), vol. 9, no. 8, pp. 1034–1042, 2008.
Z. P. Du, Q. L. Zhang, L. L. Liu. New delay-dependent robust stability of discrete singular systems with time-varying delay. Asian Journal of Control, vol. 13, no. 1, pp. 136–147, 2011.
M. Fang. Delay-dependent stability analysis for discrete singular systems with time-varying delays. Acta Automatica Sinica, vol. 36, no. 5, pp. 751–755, 2010.
Q. L. Han. A discrete delay decomposition approach to stability of linear retarded and neutral systems. Automatica, vol. 45, no. 2, pp. 517–524, 2009.
S. Zhu, Z. Li, C. Zhang. Delay decomposition approach to delay-dependent stability for singular time-delay systems. IET Control Theory and Applications, vol. 4, no. 11, pp. 2613–2620, 2010.
Z. G. Feng, J. Lam, H. J. Gao. Delay-dependent robust H∞ controller synthesis for discrete singular delay systems. International Journal of Robust and Nonlinear Control, vol. 21, no. 16, pp. 1880–1902, 2011.
X. Zhang, H. Y. Zhu. Robust stability and stabilization criteria for discrete singular time-delay LPV systems. Asian Journal of Control, vol. 14, no. 4, pp. 1084–1094, 2011.
S. Y. Xu, J. Lam. Robust Control and Filtering of Singular Systems, Berlin, Germany: Springer-Verlag, pp. 21–179, 2006.
S. Y. Xu, J. Lam, L. Q. Zhang. Robust D-stability analysis for uncertain discrete singular systems with state delay. IEEE Transactions on Circuits and Systems, Part I: Fundamental Theory and Applications, vol. 49, no. 4, pp. 551–555, 2002.
X. F. Jiang, Q. L. Han, X. H. Yu. Stability criteria for linear discrete-time systems with interval-like time-varying delay. In Proceedings of American Control Conference, IEEE, Portland, USA, pp. 2817–2822, 2005.
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This work was supported by National Natural Science Foundation of China (Nos. 61035005, 61175041, 60904009), Program for Liaoning Excellent Talents in University (No. LJQ2011118) and Natural Science Foundation of Liaoning Province (No. 201202201)
Yong-Yun Shao graduated from Shenyang Normal University (SYNU), China in 1995. He received the M. Sc. degree from SYNU in 2005. Now, he is a Ph. D. candidate at Dalian Maritime University, China. He is also an associate professor at Department of Computer and Mathematics Teaching, SYNU.
His research interests include singular delay systems, fuzzy sets and systems, and axiomatic fuzzy sets.
Xiao-Dong Liu graduated from Department of Mathematics, Northeast Normal University, China in 1986. He received the M. Sc. degree from Department of Mathematics, Jilin University, China in 1989. He received his Ph.D. degree from College of Information Science and Engineering, Northeastern University, China in 2003. He is currently a professor in Research Center of Information and Control, Dalian University of Technology, and Department of Applied Mathematics, Dalian Maritime University, a guest professor of Australian Research Council (ARC) Research Center of Excellence in Perceptive and Intelligent Machines in Complex (PIMC), Curtin University of Technology, Australia. He was a senior visiting scientist in Department of Electrical and Computer Engineering, University of Alberta, Edmonton Canada in 2003, and visiting research fellow in Department of Computing, Curtin University of Technology, Perth Australia in 2004. He has proposed axiomatic fuzzy set (AFS) theory and is a coauthor of three books. He is a recipient of the 2002 Wufu-Zhenhua Best Teacher Award of the Ministry of Communications of People’s Republic of China.
His research interests include algebra rings, combinatorics, topology molecular lattices, AFS theory and its applications, knowledge discovery and representations, data mining, pattern recognition and hitch diagnoses, analysis and design of intelligent control systems.
Xin Sun received B. Sc. and M. Sc. degrees from the Mathematics Department of Shenyang Normal University (SYNU), China in 1995 and 2006, respectively. She received her Ph.D. degree from College of Information Science and Engineering, Northeastern University, China in 2010.
She has obtained the Program for Liaoning Excellent Talents in University in 2011 and the Natural Science Foundation of Liaoning Province in 2012. She is also an associate professor at Department of Computer and Mathematics Teaching, SYNU. Her research interests include singular delay systems, AFS theory and its applications, fuzzy sets and systems, knowledge discovery and representations, data mining, pattern recognition and hitch diagnoses, analysis and design of intelligent control systems.
Zhan Su received B. Sc. degree from the College of Sciences, Northeastern University (NEU), China in 2005. She received her Ph.D. degree from College of Information Science and Engineering, Northeastern University, China in 2012.
Her research interests include practical stability theory on nonlinear system, singular systems and fuzzy control.
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Shao, YY., Liu, XD., Sun, X. et al. A new admissibility condition of discrete-time singular systems with time-varying delays. Int. J. Autom. Comput. 9, 480–486 (2012). https://doi.org/10.1007/s11633-012-0670-0
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DOI: https://doi.org/10.1007/s11633-012-0670-0