Delay-Dependent Stability Criteria for Linear Time-Delay System of Neutral Type
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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1070031Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1653
 J. Hale and S. M. V. Lunel, Introduction to Functional Differential Equations. New York: Springer-Verlag, 1993.
 J.P. Richard, "Time-delay systems: an overview of some recent advances and open problems," Automatica, vol.39, pp.1667-1694, 2003.
 M.C. de Oliveira, "Investigating duality on stability conditions," Syst. Control Lett., vol.52, pp.1-6, 2004.
 K. Gu, "An integral inequality in the stability problem of time-delay systems," in Proc. IEEE Conf. Decision Control, Sydney, Australia, Dec. 2000, pp.2805-2810.
 P.G. Park, "A Delay-Dependent Stability Criterion for Systems with Uncertain Time-Invariant Delays," IEEE Trans. Autom. Control, vol.44, pp.876-877, 1999.
 E. Fridman and U. Shaked, "An Improved Stabilization Method for Linear Time-Delay Systems," IEEE Trans. Autom. Control, vol.47, pp.1931- 1937, 2002.
 E. Fridman and U. Shaked, "Delay-dependent stability and H∞ control: constant and time-varying delays," Int. J. Control, vol.76, pp.48-60, 2003.
 S. Xu, J. Lam, and Y. Zou, "Simplified descriptor system approach to delay-dependent stability and performance analyses for time-delay systems," IEE Proc.-Control Theory Appl., vol.152, pp.147-151, 2005.
 S. Xu and J. Lam, "Improved Delay-Dependent Stability Criteria for Time-Delay Systems," IEEE Trans. Autom. Control, vol.50, pp.384-387, 2005.
 O.M. Kwon and Ju H. Park, "On Improved Delay-Dependent Robust Control for Uncertain Time-Delay Systems," IEEE Trans. Autom. Control, vol.49, pp.1991-1995, 2004.
 P.G. Park and J.W. Ko, "Stability and robust stability for systems with a time-varying delay," Automatica, vol.43, pp.1855-1858, 2007.
 Y. Ariba and F. Gouaisbaut, "An augmented model for robust stability analysis of time-varying delay systems," Int. J. Control, vol.82, pp.1616- 1626, 2009.
 J.H. Park and S. Won, "Asymptotic Stability of Neutral Systems with Multiple Delays," J. Optim. Theory Appl., vol.103, pp.183-200, 1999.
 M. Wu, Y. He, and J.-H. She, "New Delay-Dependent Stability Criteria and Stabilizing Method for Neutral Systems," IEEE Trans. Autom. Control, vol.49, pp.2266-2271, 2004.
 D. Yue and Q.-L. Han, "A Delay-Dependent Stability Criterion of Neutral Systems and its Application to a Partial Element Equivalent Circuit Model," IEEE Trans. Circuits Syst. II-Express Briefs, vol.51, pp.685-689, 2004.
 S. Xu, J. Lam, and Y. Zou, "Further results on delay-dependent robust stability conditions of uncertain neutral systems," Int. J. Robust Nonlinear Control, vol.15, pp.233-246, 2005.
 Ju H. Park and O. Kwon, "On new stability criterion for delaydifferential systems of neutral type," Appl. Math. Comput., vol.162, pp.627-637, 2005.
 Z. Zhao, W. Wang, and B. Yang, "Delay and its time-derivative dependent robust stability of neutral control system," Appl. Math. Comput., vol.187, pp.1326-1332, 2007.
 O.M. Kwon, Ju H. Park, and S.M. Lee, "On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays," Appl. Math. Comput., vol.197, pp.864-873, 2008.
 O.M. Kwon and Ju H. Park, "Augmented Lyapunov functional approach to stability of uncertain neutral systems with time-varying delays," Appl. Math. Comput., vol.207, pp.202-212, 2009.
 M.N.A. Parlakci, "Extensively augmented Lyapunov functional approach for the stability of neutral time-delay systems," IET Contr. Theory Appl., vol.2, pp.431-436, 2008.
 X. Nian, H. Pang, W. Gui, and H. Wang, "New stability analysis for linear neutral system via state matrix decomposition," Appl. Math. Comput., vol.215, pp.1830-1837, 2009.
 A. Bellen, N. Guglielmi, and A.E. Ruehli, "Methods for Linear Systems of Circuit Delay Differential Equations of Neutral Type," IEEE Trans. Circuits Syst. I-Regul. Pap., vol.46, pp.212-216, 1999.
 S.I. Niculescu and B. Brogliato, "Force measurements time-delays and contact instability phenomenon," Eur. J. Control, vol.5, pp.279-289, 1999.
 S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia: SIAM, 1994.
 P. Gahinet, A. Nemirovskii, A. Laub, and M. Chilali, LMI Control Toolbox User-s Guide. Natick, Massachusetts: The MathWorks, Inc., 1995.