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Delay-Dependent Robust Stability of Uncertain Time-Delayed Linear Systems  

Yi, Yearn-Gui (충북대학교 대학원 제어계측공학과)
Kim, Jin-Hoon (충북대학교 전기전자공학부)
Publication Information
The Transactions of the Korean Institute of Electrical Engineers D / v.55, no.4, 2006 , pp. 147-153 More about this Journal
Abstract
In this paper, we propose a new delay-dependent criterion on the robust stability of time-delayed linear systems having norm bounded uncertainties. Based on new form of Lyapunov-Krasovskii functional and the Newton-Leibniz formula, we drive a result in the form of LMI which guarantees the robust stability without any model transformation. The Newton-Leibniz equation was used to relate the cross terms with free matrices. Finally, we show the usefulness of our result by two numerical examples.
Keywords
Uncertainty; Time-Delay; Robust Stability; Lyapunov-Krasovskii Functional; LMI;
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1 Y.S. Lee, Y.S. Moon, W.H. Kwon and P.G. Park 'Delay-dependent robust H1 control for uncertain systems with a state-delay,' Automatica, Vol. 40, PP. 65-72, Jan, 2004   DOI   ScienceOn
2 W. J. Rogh, Linear System Theory. Upper Saddle River, New Jersey:Prentice Hall, 1996
3 S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory. Philadelphia, PA : SIAM, 1994
4 Y. He, M. Wu, J. H. She and G. P. Liu 'Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties,' IEEE. Trans. Autom. Control, Vol. 49, no. 5, PP. 789-792, May, 2004   DOI   ScienceOn
5 Y. S. Moon, P. Park, W. H. Kwon and Y. S. Lee, 'Delay-dependent robust stabilization of uncertain state-delayed systems,' Int. J. Control, Vol. 74 PP. 1447-1455, 2001   DOI   ScienceOn
6 M. S. Mahmoud and A. Ismail 'New results on delay-dependent control of time-delay systems,' IEEE. Trans. Autom. Control, Vol. 50, no. 1, PP. 95-100, Jan, 2005   DOI
7 X. M. Zhang, M. Wu, J. H. She and Y. He 'Delay-dependent stabilization of linear systems with time-varying state and input delays,' Automatica, Vol. 41, PP. 1405-1412, May, 2005   DOI   ScienceOn
8 X. Li and C. E. de Souza, 'Delay-dependent robust stability and stabilization of uncertain linear delay systems : A linear matrix inequality approach,' IEEE Trans. Autom. Control, Vol. 42, no. 8, PP. 1144-1148, Aug. 1997   DOI   ScienceOn
9 M. Wu, Y. He, J. H. She and G. P. Liu 'Delay-dependent criteria for robust stability of time-varying delay systems,' Automatica, Vol. 40, PP. 1435-1439, Mar, 2004   DOI   ScienceOn
10 S. Xu and J. Lam 'Improved delay-dependent stability criteria for time-delay systems,' IEEE. Trans. Autom. Control, Vol. 50, no. 3, PP. 384-387, Mar, 2005   DOI   ScienceOn
11 Niculescu, S.-I., Neto, A. T., Dion, J.-M., and Dugard, L., 1995, 'Delay-Dependent Stability of Linear Systems with Delayed state : an LMI Approach,' Proc. 34th IEEE Conf. on Decision and Control, PP. 1495-1497   DOI
12 E. Fridman and U. Shaked, 'An improved stabilization method for linear time-delay systems,' IEEE Trans. Autom. Control, Vol. 47, no. 11, PP. 1931-1937, Nov. 2002   DOI   ScienceOn
13 E. Fridman and U. Shaked, 'New bounded real lemma for time-delay systems and their applications,' IEEE Trans. Autom. Control, vol. 46, no. 12, PP. 1973-1978, Dec. 2001   DOI   ScienceOn
14 H. Gao and C. Wang, 'Delay-dependent robust $H_{\infty}$ and $L_1$ - $L_2$ filtering for a class of uncertain nonlinear time-delay systems,' IEEE. Trans. Autom. Control, Vol. 48, no. 9, PP. 1661-1666, Sep, 2003   DOI   ScienceOn
15 Y. xia and Y. Jia, 'Robust control of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functionals,' Syst. Control Lett., Vol. 50, PP. 183-193, 2003   DOI   ScienceOn
16 S.-I. Niculescu, 'Memoryless control with an ${\alpha}$-stability constrint for time-delay systems : An LMI approach,' IEEE. Trans. Autom. Control, Vol. 43, no. 5, PP. 739-743, May, 1998   DOI   ScienceOn
17 J. H. Kim, 'Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty,' IEEE. Trans. Autom. Control, Vol. 46, no. 5, PP. 789-792, May, 2001   DOI   ScienceOn
18 P. Park, 'A delay-dependent stability criterion for system with uncertain time-invariant delays,' IEEE. Trans. Autom. Control, Vol. 44,no. 4, PP. 876-877, Apr, 1999   DOI   ScienceOn