Novel Stabilization for Systems with Two Additive Time-Varying Delays

Article Preview

Abstract:

This paper provides a new delay-dependent stabilization criterion for systems with two additive time-varying delays. The novel functional is constructed, a tighter upper bound of the derivative of the Lyapunov functional is obtained. These results have advantages over some existing ones in that the skillfully combination of the delay decomposition and reciprocally convex approach. Two examples are provided to demonstrate the less conservatism and effectiveness of the results in this paper.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

523-533

Citation:

Online since:

August 2014

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2014 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

* - Corresponding Author

[1] Hale.J. Functional differential equations, New York: Springer-Verlag, (1977).

Google Scholar

[2] K.Q. Gu. An integral inequality in the stability problem of time-delay system. Proceedings of 39th IEEE Conference on Decision and Control 39, 2000, 2805–2810.

Google Scholar

[3] E. Fridman, U. Shaked. An improved stabilization method for linear time-delay systems. IEEE Transactions on Automatic Control, 47(2002) 1931-(1937).

DOI: 10.1109/tac.2002.804462

Google Scholar

[4] J.P. Richard. Time-delay systems: An overview of some recent advances and open problems. Automatica 39(2003) 1667–1694.

DOI: 10.1016/s0005-1098(03)00167-5

Google Scholar

[5] M. Wu, Y. He, J. H. She and G. P. Liu. Delay-dependent criteria for robust stability of time -varying delay systems. Automatica, 40(2004) 1435-1439.

DOI: 10.1016/j.automatica.2004.03.004

Google Scholar

[6] H.Y. Shao. Delay-dependent approaches to globally exponential stability for recurrent neural network. IEEE transcations on Circuits Systems II, 55(2008) 591–595.

DOI: 10.1109/tcsii.2007.916727

Google Scholar

[7] H.Y. Shao. New Delay-dependent stability criteria for systems with interval delay. Automatica, 45(2009) 744–749.

DOI: 10.1016/j.automatica.2008.09.010

Google Scholar

[8] R. Sipahi, T. Vyhlłdal, S. -I. Niculescu, Pierdomenico Pepe. Time Delay Systems: Methods, Applications and New Trends. Springer, (2012).

Google Scholar

[9] Y. He, Q. -G. Wang, C. Lin, M. Wu. Delay-range-dependent stability for systems with time- varying delay. Automatica 43(2007) 371–376.

DOI: 10.1016/j.automatica.2006.08.015

Google Scholar

[10] Y. Xia, Y. Jia. Robust stability functionals of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functions. International Journal of Control, 75 (2002) 1427–1434.

DOI: 10.1080/0020717021000023834

Google Scholar

[11] C. Hua, X. Guan, P. Shi. Robust backstepping control for a class of time delayed systems. IEEE Transactions on Automatic Control, 50(2005) 894–899.

DOI: 10.1109/tac.2005.849255

Google Scholar

[12] X. -M. Zhang, M. Wu, J. -H. She, Y. He. Delay-dependent stabilization of linear systems with time-varying state and input delays. Automatica, 41(2005) 1405–1412.

DOI: 10.1016/j.automatica.2005.03.009

Google Scholar

[13] H. Gao, C. Wang. A delay-dependent approach to robust H1filtering for uncertain discrete-time state-delayed systems. IEEE Transactions of Signal Processing, 52(2004) 1631–1640.

DOI: 10.1109/tsp.2004.827188

Google Scholar

[14] H. Liu, F. Sun, K. He, Z. Sun. Design of reduced-order H1 filter for Markovian jumping systems with time delay. IEEE Transactions on Circuits and Systems (II), 51(2004) 607–612.

DOI: 10.1109/tcsii.2004.836882

Google Scholar

[15] S. Xu, J. Lam, S. Huang, C. Yang. H1 model reduction for linear time-delay systems: Continuous-time case. International Journal of Contro, 74(2001) 1062–1074.

DOI: 10.1080/00207170110052194

Google Scholar

[16] J. Lam, H. Gao, C. Wang. Stability analysis for continuous system with two additive time-varying delay components. System and Control Letters, 56(2007) 16-24.

DOI: 10.1016/j.sysconle.2006.07.005

Google Scholar

[17] H. Gao, T. Chen, J. Lam. A new delay system approach to network-based control. Automatica, 44(2008) 39–52.

DOI: 10.1016/j.automatica.2007.04.020

Google Scholar

[18] H. Wua, X. Liao,W. Feng, S. Guo,W. Zhang, Robust stability analysis of uncertain systems with two additive time-varying delay components, Applied Mathematical Modelling, 33(2009)4345-4353.

DOI: 10.1016/j.apm.2009.03.008

Google Scholar

[19] H.Y. Shao, Z.Q. Zhang, Stability and stabilization for systems with two additive time-varying delay components. Proceedings of the 30th Chinese Control Conference, July 22-24, 2011, Yantai, China, 1119–1124.

Google Scholar

[20] Rajeeb Dey, G. Ray, Sandip Ghosh, A. Rakshit, Stability analysis for continuous system with additive time-varying delays: A less conservative result. Applied Mathematics and Computation 215(2010) 3740–3745.

DOI: 10.1016/j.amc.2009.11.014

Google Scholar

[21] X.L. Zhu, X. Du. New results of stability analysi for systems with two additive time-varying delays. Proceedings of the 31th Chinese Control Conference, July 25-27, 2012, Hefei, China, 1452–1457.

Google Scholar

[22] PooGyeon Park, Jeong Wan Ko, Changki Jeong, Reciprocally convex approach to stability of systems with time-varying delays. Automatica, 47(2011) 235–238.

DOI: 10.1016/j.automatica.2010.10.014

Google Scholar