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.
[1] J. Hale and S. M. V. Lunel, Introduction to Functional Differential
Equations. New York: Springer-Verlag, 1993.
[2] J.P. Richard, "Time-delay systems: an overview of some recent advances
and open problems," Automatica, vol.39, pp.1667-1694, 2003.
[3] M.C. de Oliveira, "Investigating duality on stability conditions," Syst.
Control Lett., vol.52, pp.1-6, 2004.
[4] 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.
[5] 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.
[6] E. Fridman and U. Shaked, "An Improved Stabilization Method for Linear
Time-Delay Systems," IEEE Trans. Autom. Control, vol.47, pp.1931-
1937, 2002.
[7] 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.
[8] 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.
[9] S. Xu and J. Lam, "Improved Delay-Dependent Stability Criteria for
Time-Delay Systems," IEEE Trans. Autom. Control, vol.50, pp.384-387,
2005.
[10] 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.
[11] 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.
[12] 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.
[13] J.H. Park and S. Won, "Asymptotic Stability of Neutral Systems with
Multiple Delays," J. Optim. Theory Appl., vol.103, pp.183-200, 1999.
[14] 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.
[15] 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.
[16] 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.
[17] 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.
[18] 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.
[19] 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.
[20] 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.
[21] 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.
[22] 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.
[23] 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.
[24] S.I. Niculescu and B. Brogliato, "Force measurements time-delays and
contact instability phenomenon," Eur. J. Control, vol.5, pp.279-289, 1999.
[25] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix
Inequalities in System and Control Theory. Philadelphia: SIAM, 1994.
[26] P. Gahinet, A. Nemirovskii, A. Laub, and M. Chilali, LMI Control
Toolbox User-s Guide. Natick, Massachusetts: The MathWorks, Inc.,
1995.
[1] J. Hale and S. M. V. Lunel, Introduction to Functional Differential
Equations. New York: Springer-Verlag, 1993.
[2] J.P. Richard, "Time-delay systems: an overview of some recent advances
and open problems," Automatica, vol.39, pp.1667-1694, 2003.
[3] M.C. de Oliveira, "Investigating duality on stability conditions," Syst.
Control Lett., vol.52, pp.1-6, 2004.
[4] 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.
[5] 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.
[6] E. Fridman and U. Shaked, "An Improved Stabilization Method for Linear
Time-Delay Systems," IEEE Trans. Autom. Control, vol.47, pp.1931-
1937, 2002.
[7] 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.
[8] 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.
[9] S. Xu and J. Lam, "Improved Delay-Dependent Stability Criteria for
Time-Delay Systems," IEEE Trans. Autom. Control, vol.50, pp.384-387,
2005.
[10] 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.
[11] 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.
[12] 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.
[13] J.H. Park and S. Won, "Asymptotic Stability of Neutral Systems with
Multiple Delays," J. Optim. Theory Appl., vol.103, pp.183-200, 1999.
[14] 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.
[15] 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.
[16] 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.
[17] 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.
[18] 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.
[19] 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.
[20] 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.
[21] 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.
[22] 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.
[23] 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.
[24] S.I. Niculescu and B. Brogliato, "Force measurements time-delays and
contact instability phenomenon," Eur. J. Control, vol.5, pp.279-289, 1999.
[25] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix
Inequalities in System and Control Theory. Philadelphia: SIAM, 1994.
[26] P. Gahinet, A. Nemirovskii, A. Laub, and M. Chilali, LMI Control
Toolbox User-s Guide. Natick, Massachusetts: The MathWorks, Inc.,
1995.
@article{"International Journal of Information, Control and Computer Sciences:57061", author = "Myeongjin Park and Ohmin Kwon and Juhyun Park and Sangmoon Lee", title = "Delay-Dependent Stability Criteria for Linear Time-Delay System of Neutral Type", 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.
", keywords = "Neutral systems, Time-delay, Stability, Lyapunovmethod, LMI.", volume = "4", number = "10", pages = "1540-5", }
