Delay-Dependent Absolute Stability Analysis of Lurie Control System with Multiple Delays

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Abstract:

This paper investigates the stability problem for Lurie control system with multiple delays. The system with multiple time-delays is transformed, then the delay divided into several segments, a novel Lyapunov functional is introduced and some new delay-dependent stability criteria are derived by employed integral-equality technique. It is theoretically proved that the obtained criteria are less conservative than some existing ones. An example is given to illustrate the effectiveness of the proposed results.

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Advanced Materials Research (Volumes 631-632)

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1195-1200

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January 2013

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© 2013 Trans Tech Publications Ltd. All Rights Reserved

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[1] J. K. Hale, Theory of Functional Differential Equation, Springer, New York, (1977).

Google Scholar

[2] J. K. Hale S.M. VerduynLunel, Introductiont of unctional differential equations , in : Applied Mathe matical Sciences , Springer-Verlag , NewYork, (1993).

Google Scholar

[3] Y. He, Q. G. Wang, L. H. Xie, C. Lin, Further improvemen of free-weighting matrices technique for systems with time-varying delay, IEEE Trans. Automat. Control52(2007)293–299.

DOI: 10.1109/tac.2006.887907

Google Scholar

[4] Y. He, M. Wu, J.H. She, G.P. Liu, Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic type uncertainties, IEEE Trans. Automat. Control 49(2004)828–832.

DOI: 10.1109/tac.2004.828317

Google Scholar

[5] M. Wu, Y. He, J.H. She, New delay-dependent stability criteria and stabilizing method for neutral systems, IEEE Trans. Automat. Control 49(2004) 2266–2271.

DOI: 10.1109/tac.2004.838484

Google Scholar

[6] L. Yu, Q. L. Han, S. Yu, J. Gao, Delay-dependent conditions for robust absolute stability of uncertain time-delay systems, in: Proc. 42nd IEEE Conf. on Decision and Control. Maui, Hawaii, USA, 2003, p.6033–6037.

DOI: 10.1109/cdc.2003.1272192

Google Scholar

[7] J. W. Cao, S. M. Zhong, Y. Y. Hu, Delay-dependent condition for absolute stability of Lurie control systems with multiple time delays and nonlinearities, J. Math . Anal . Appl. 338(2008)497–504.

DOI: 10.1016/j.jmaa.2007.05.039

Google Scholar

[8] Xiaohong Nian, Delay dependent conditions for absolute stability of Lurie type control systems, Acta Automat. Sinica 25 (1999) 556–564.

Google Scholar

[9] J. W. Cao, S. M. Zhong, New delay-dependent condition for absolute stability of Lurie control systems with multiple time-delays and nonlinearities, Appl. Math. Comput. 194 (2007)250–258.

DOI: 10.1016/j.amc.2007.04.034

Google Scholar

[10] FangQiu, QuanxinZhang. Absolute stability analysis of Lurie control system with multiple delays: Anintegral-equalityapproach[J]. Nonlinear Analysis: Real World Applications 12 (2011) 1475–1484.

DOI: 10.1016/j.nonrwa.2010.10.007

Google Scholar

[11] Junkang Tian, Shouming Zhong, Lianglin Xiong. Delay-dependent absolute stability of Lurie control systems with multiple time-delays[J]. Applied Mathematics and Computation , 188 (2007) 379–384.

DOI: 10.1016/j.amc.2006.09.119

Google Scholar

[12] J. F. Gao, H. Y. Su, X. F. Ji, J. Chu, New delay-dependent absolute stability criteria for Lurie control systems, Acta. Automat. Sinica. 34(2008)1275–1280.

DOI: 10.3724/sp.j.1004.2009.01275

Google Scholar

[13] Q. L. Han, Absolute stability of time-delay systems with sector bounded nonlinearity, Automatica 41(2005)2171–2176.

DOI: 10.1016/j.automatica.2005.08.005

Google Scholar