{"title":"Delay-Dependent Stability Criteria for Linear Time-Delay System of Neutral Type","authors":"Myeongjin Park, Ohmin Kwon, Juhyun Park, Sangmoon Lee","volume":46,"journal":"International Journal of Computer and Information Engineering","pagesStart":1602,"pagesEnd":1607,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/7980","abstract":"
This paper proposes improved delay-dependent stability conditions of the linear time-delay systems of neutral type. The proposed methods employ a suitable Lyapunov-Krasovskii’s functional and a new form of the augmented system. New delay-dependent stability criteria for the systems are established in terms of Linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Numerical examples showed that the proposed method is effective and can provide less conservative results.<\/p>\r\n","references":"[1] J. Hale and S. M. V. Lunel, Introduction to Functional Differential\r\nEquations. New York: Springer-Verlag, 1993.\r\n[2] J.P. Richard, \"Time-delay systems: an overview of some recent advances\r\nand open problems,\" Automatica, vol.39, pp.1667-1694, 2003.\r\n[3] M.C. de Oliveira, \"Investigating duality on stability conditions,\" Syst.\r\nControl Lett., vol.52, pp.1-6, 2004.\r\n[4] K. Gu, \"An integral inequality in the stability problem of time-delay\r\nsystems,\" in Proc. IEEE Conf. Decision Control, Sydney, Australia, Dec.\r\n2000, pp.2805-2810.\r\n[5] P.G. Park, \"A Delay-Dependent Stability Criterion for Systems with\r\nUncertain Time-Invariant Delays,\" IEEE Trans. Autom. Control, vol.44,\r\npp.876-877, 1999.\r\n[6] E. Fridman and U. Shaked, \"An Improved Stabilization Method for Linear\r\nTime-Delay Systems,\" IEEE Trans. Autom. Control, vol.47, pp.1931-\r\n1937, 2002.\r\n[7] E. Fridman and U. Shaked, \"Delay-dependent stability and H\u221e control:\r\nconstant and time-varying delays,\" Int. J. Control, vol.76, pp.48-60, 2003.\r\n[8] S. Xu, J. Lam, and Y. Zou, \"Simplified descriptor system approach\r\nto delay-dependent stability and performance analyses for time-delay\r\nsystems,\" IEE Proc.-Control Theory Appl., vol.152, pp.147-151, 2005.\r\n[9] S. Xu and J. Lam, \"Improved Delay-Dependent Stability Criteria for\r\nTime-Delay Systems,\" IEEE Trans. Autom. Control, vol.50, pp.384-387,\r\n2005.\r\n[10] O.M. Kwon and Ju H. Park, \"On Improved Delay-Dependent Robust\r\nControl for Uncertain Time-Delay Systems,\" IEEE Trans. Autom. Control,\r\nvol.49, pp.1991-1995, 2004.\r\n[11] P.G. Park and J.W. Ko, \"Stability and robust stability for systems with\r\na time-varying delay,\" Automatica, vol.43, pp.1855-1858, 2007.\r\n[12] Y. Ariba and F. Gouaisbaut, \"An augmented model for robust stability\r\nanalysis of time-varying delay systems,\" Int. J. Control, vol.82, pp.1616-\r\n1626, 2009.\r\n[13] J.H. Park and S. Won, \"Asymptotic Stability of Neutral Systems with\r\nMultiple Delays,\" J. Optim. Theory Appl., vol.103, pp.183-200, 1999.\r\n[14] M. Wu, Y. He, and J.-H. She, \"New Delay-Dependent Stability Criteria\r\nand Stabilizing Method for Neutral Systems,\" IEEE Trans. Autom.\r\nControl, vol.49, pp.2266-2271, 2004.\r\n[15] D. Yue and Q.-L. Han, \"A Delay-Dependent Stability Criterion of\r\nNeutral Systems and its Application to a Partial Element Equivalent\r\nCircuit Model,\" IEEE Trans. Circuits Syst. II-Express Briefs, vol.51,\r\npp.685-689, 2004.\r\n[16] S. Xu, J. Lam, and Y. Zou, \"Further results on delay-dependent robust\r\nstability conditions of uncertain neutral systems,\" Int. J. Robust Nonlinear\r\nControl, vol.15, pp.233-246, 2005.\r\n[17] Ju H. Park and O. Kwon, \"On new stability criterion for delaydifferential\r\nsystems of neutral type,\" Appl. Math. Comput., vol.162,\r\npp.627-637, 2005.\r\n[18] Z. Zhao, W. Wang, and B. Yang, \"Delay and its time-derivative dependent\r\nrobust stability of neutral control system,\" Appl. Math. Comput.,\r\nvol.187, pp.1326-1332, 2007.\r\n[19] O.M. Kwon, Ju H. Park, and S.M. Lee, \"On stability criteria for\r\nuncertain delay-differential systems of neutral type with time-varying\r\ndelays,\" Appl. Math. Comput., vol.197, pp.864-873, 2008.\r\n[20] O.M. Kwon and Ju H. Park, \"Augmented Lyapunov functional approach\r\nto stability of uncertain neutral systems with time-varying delays,\" Appl.\r\nMath. Comput., vol.207, pp.202-212, 2009.\r\n[21] M.N.A. Parlakci, \"Extensively augmented Lyapunov functional approach\r\nfor the stability of neutral time-delay systems,\" IET Contr. Theory Appl.,\r\nvol.2, pp.431-436, 2008.\r\n[22] X. Nian, H. Pang, W. Gui, and H. Wang, \"New stability analysis\r\nfor linear neutral system via state matrix decomposition,\" Appl. Math.\r\nComput., vol.215, pp.1830-1837, 2009.\r\n[23] A. Bellen, N. Guglielmi, and A.E. Ruehli, \"Methods for Linear Systems\r\nof Circuit Delay Differential Equations of Neutral Type,\" IEEE Trans.\r\nCircuits Syst. I-Regul. Pap., vol.46, pp.212-216, 1999.\r\n[24] S.I. Niculescu and B. Brogliato, \"Force measurements time-delays and\r\ncontact instability phenomenon,\" Eur. J. Control, vol.5, pp.279-289, 1999.\r\n[25] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix\r\nInequalities in System and Control Theory. Philadelphia: SIAM, 1994.\r\n[26] P. Gahinet, A. Nemirovskii, A. Laub, and M. Chilali, LMI Control\r\nToolbox User-s Guide. Natick, Massachusetts: The MathWorks, Inc.,\r\n1995.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 46, 2010"}