A Novel Stability Criterion of Lur’e Systems with Time-Varying Delay Based on Relaxed Conditions
Peng Zhang, Pitao Wang, and Tao Shen
School of Electrical Engineering, University of Jinan
No.336, West Road of Nan Xinzhuang, Jinan, Shandong 250022, China
This paper considers the absolute stability for Lur’e systems with time-varying delay and sector-bounded nonlinear. In this paper, a new relaxed condition based on delay decomposition approach is proposed. By using this technique and employing some inequality, the new delay-dependent stability criteria for Lur’e systems are derived in the form of linear matrix inequalities (LMIs). A numerical example is presented to show less conservatism of proposed methods compared with the previous.
-  A. I. Lur’e, “Some nonlinear problems in the theory of automatic control,” Her Majesty’s Stationery Office, 1957.
-  Z. Tai and S. Lun, “Absolutely exponential stability of Lur’e distributed parameter control systems,” Appl. Mathe. Letters, Vol.25, No.3, pp. 232-236, 2012.
-  C. A. C. Gonzaga, M. Jungers, and J. Daafouz, “Stability analysis of discrete-time Lur’e systems,” Automatica, Vol.48, pp. 2277-2283, 2012.
-  D. Zhang, Y. Li, and A. Z. Wen, “Stability and guaranteed cost control for uncertain time-delay Lur’e systems,” J. Sys. Eng. Elect., Vol.19, No.3, pp. 546-554, 2008.
-  A. Seuret and F. Gouaisbaut, “Wirtinger-based integral inequality: Application to time-delay systems,” Automatica, Vol.49, No.9, pp. 2860-2866, 2013.
-  M. Khodabakhshian, L. Feng, and J. Wikander, “One-step prediction for Improving gear changing control of HEVs,” J. Robot. Mechatron., Vol.26, No.6, pp. 799-808, 2014.
-  Z. Guan, S. Wakitani, and T. Yamamoto, “Design and experimental evaluation of a date-oriented generalized predictive PID controller,” J. Robot. Mechatron., Vol.28, No.5, pp. 799-808, 2014.
-  T. H. Lee, H. P. Ju, and S. Xu, “Relaxed conditions for stability of time-varying delay systems,” Automatica, Vol.75, pp. 11-15.
-  P. Liu, “Delayed decomposition approach to robust absolute stability of Lur’e control system with time-varying delay,” Appl. Math. Model., Vol.40, No.3, pp. 722-729, 2016.
-  P. Li, Z. Bao, and W. Yan, “New delay-dependent absolute stability for uncertain Lur’e system with interval delay,” Proc. of the 10th World Congress on Intelligent Control and Automation, pp. 1062-1066, 2012.
-  Q. L. Han, “Absolute stability of time-delay systems with sector-bounded nonlinearity,” Automatica, Vol.41, No.12, pp. 2171-2176, 2005.
-  Q. L. Han and D. Yue, “Absolute stability of Lur’e systems with time-varying delay,” IET Control Theory Appl., Vol.1, No.3, pp. 854-859, 2007.
-  J. F. Gao, H. P. Pan, and X. F. Ji, “A New Delay-Dependent Absolute Stability Criterion for Lurie Systems with Time-Varying Delay,” Acta Auto. Sinica, Vol.36, No.6, pp. 845-850, 2010.
-  W. Duan, Z. Liu, and X. Yang, “Improved Robust Stability Criteria for Time-Delay Lur’e System,” Asian J. Control, Vol.19, No.1, pp. 139-150, 2017.
-  J. Cao, H. X. Li, and D. Ho, “Synchronization criteria of Lur’e systems with time-delay feedback control,” Chaos Solitons Fractals, Vol.23, No.4, pp. 1285-1298, 2005.
-  L. Yu, Q. L. Han, S. Yu, and J. Gao, “Delay-dependent conditions for robust absolute stability of uncertain time-delay systems,” 42nd IEEE Int. Conf. on Decision and Control, Vol.6, pp. 6033-6037, 2003.
-  J. H. Kim, “Further improvement of Jensen inequality and application to stability of time-delayed systems,” Automatica, Vol.64, pp. 121-125, 2016.
-  Y. Wang, Y. He, and X. Zhang, “Refined delay-dependent robust stability criteria of a class of uncertain mixed neutral and Lur’e dynamical systems with interval time-varying delays and sector-bounded nonlinearity,” Nonlinear Anal.- Real World Appl., Vol.13, No.5, pp. 2188-2194, 2012.
-  B. Zhang, J. Lam, and S. Xu, “Relaxed results on reachable set estimation of time-delay systems with bounded peak inputs,” Int. J. Ro. Non. Control, Vol.26, No.9, pp. 1994-2007, 2016.
-  W. Duan, B. Du, Z. Liu, and Y. Zou, “Improved Stability Criteria for Uncertain Neutral-Type Lur’e Systems with Time-Varying Delays,” J. Frankl. Inst., Vol.351, No.9, pp. 4538-4554, 2014.
-  X. Zhang, B. Cui, and W. Li, “A delay decomposition approach to absolute stability of Lurie control system with time-varying delay,” 2012 24th Chinese Control and Decision Conf., pp. 3062-3067, 2012.
-  A. Kazemy and M. Farrokhi, “Robust Absolute Stability Analysis of Multiple Time-Delay Lur’e Systems With Parametric Uncertainties,” Asian J. Control, Vol.15, No.1, pp. 203-213, 2013.
-  P. Mukhija, I. N. Kar, and R. K. P. Bhatt, “Robust Absolute Stability Criteria for Uncertain Lurie System with Interval Time-Varying Delay,” J. Dyna. Sys. Measurement Control, Vol.136, No.4, p. 041020, 2014.
-  X. M. Zhang, Q. L. Han, A. Seuret, and F. Gouaisbaut, “An improved reciprocally convex inequality and an augmented Lyapunov-Krasovskii functional for stability of linear systems with time-varying delay,” Automatica, Vol.84, pp. 221-226, 2017.