Improved Asymptotic Stability Criteria for Uncertain Neutral Systems with Time-varying Discrete Delays
This paper investigates the robust stability of uncertain neutral system with time-varying delay. By using Lyapunov method and linear matrix inequality technology, new delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs), which can be easy to check the robust stability of the considered systems. Numerical examples are given to indicate significant improvements over some existing results.
[1] S. Boyd, L.El. Ghaoui, E. Feron and V. Balakrishnan, Linear matrix
inequalities in systems and control theory. Philadelphia: SIAM 1994.
[2] J.K. Hale, S.M. & Verduyn Lunel, Introduction to functional differential
equation, New York: Springer 1993; 292-293.
[3] V. Kapila, W.M. Haddad, Memoryless H1 controllers for discrete time
systems with time delay, Automatica, vol. 35, pp. 1443-1451, 1998.
[4] J.X. Kuang, H.J. Tian, Taketomo Mitsui, Asymptotic and numerical
stability of systems of neutral differential equations with many delays.
Journal of Computational and Applied Mathematics, vol. 223, pp. 614-
625, 2009.
[5] H. Li, S.-M. Zhong, H.-b. Li, Some new simple stability criteria of linear
neutral systems with a single delay, Journal of Computational and Applied
Mathematics, vol. 200, pp. 441-447, 2007.
[6] S.Y. Xu, J. Lam, D.W.C. Ho,Y. Zou, Delay-dependent exponential
stability for a class of neural networks with time delays, Journal of
Computational and Applied Mathematics, vol. 183, pp. 16-28, 2005.
[7] C.-C. Shen, S.-M. Zhong, New delay-dependent robust stability criterion
for uncertain neutral systems with time-varying delay and nonlinear
uncertainties, Chaos, Solitons & Fractals vol. 40, pp. 2277-2285, 2009.
[8] Ji.F. Gao, H.Y. Su, X.F. Ji, J. Chu, Stability analysis for a class of neutral
systems with mixed delays and sector-bounded nonlinearity, Nonlinear
Analysis: Real World Applications, vol. 9, pp. 2350-2360, 2008.
[9] Ju.H. Park. Novel robust stability criterion for a class of neutral systems
with mixed delays and nonlinear perturbations. Applied Mathematics and
Computation, vol. 161, pp. 413-421, 2005.
[10] Q.-L. Han, On stability of linear neutral systems with mixed time delays:
A discretized Lyapunov functional approach, Automatica, vol. 41, pp.
1209-1218, 2005.
[11] Q.-L. Han, A descriptor system approach to robust stability of uncertain
neutral systems with discrete and distributed delays. IEEE Transactions
on Automatic Control, vol. 49, pp. 1791-1796, 2004.
[12] D.Y. Liu, X.Z. Liu, S.M. Zhong, Delay-dependent robust stability and
control synthesis for uncertain switched neutral systems with mixed
delays. Applied Mathematics and Computation, vol. 202, pp, 828-839,
2008.
[13] K.Q. Gu, S.I. Niculescu, Additional dynamics in transformed time-delay
systems, IEEE Trans. Autom. Control, vol. 45, pp. 572-575, 2000.
[14] Q.-L. Han, On robust stability of neutral systems with time-varying
discrete delay and norm-bounded uncertainty, IEEE Transactions on
Automatic Control, vol. 40, pp. 1087-1092, 2004.
[15] Z.R. Zhao, W. Wang, Bin Yang, Delay and its time-derivative dependent
robust stability of neutral control system, Applied Mathematics and
Computation, vol. 187, pp. 1326-1332, 2007.
[16] K. Wei, C.-H. Lie, Stability criteria for uncertain systems with interval
time-varying delays, Chaos, Solitons & Fractals, Available online vol. 38
pp. 650-657, 2008.
[17] O.M. Kwon, Ju.H. Park, S.M. Lee, On stability criteria for uncertain
delay-differential systems of neutral type with time-varying delays, Applied
Mathematics and Computation, vol. 197 pp. 864-873, 2008.
[18] J.-H. Kim, Delay and its time-derivative dependent robust stability
of time-delayed linear systems with uncertainty, IEEE Transactions on
Automatic Control, vol. 46 pp. 789-792, 2001.
[19] Y. He, M. Wu, Jin-Hua She, Guo-Ping Liu, Delay-dependent robust
stability criteria for uncertain neutral systems with mixed delays, Systems
& Control Letters, vol. 51 pp. 57-65, 2004.
[20] E. Fridman, U. Shaked, An improved approach stabilization method
for linear systems, IEEE Transactions on Automatic Control, vol. 47 pp.
1931-1937, 2002.
[21] M. Wu, Y. He, Jin-Hua She, Guo-Ping Liu, Delay-dependent criteria for
robust stability of time-varying delay systems, Automaticat, vol. 40 pp.
1435-1439, 2004.
[22] H.C. Yan, X.H. Huang, H. Zhang, M. Wang, Delay-dependent robust
stability criteria of uncertain stochastic systems with time-varying delay,
Chaos, Solitons & Fractals, vol. 40, pp. 1668-1679, 2009.
[23] Ju.H. Park, O. Kwon, On new stability criterion for delay-differential
systems of neutral type, Applied Mathematics and Computation, vol. 162;
pp. 627-637, 2005.
[24] X.-G. Liu, M. Wu, Ralph Martin, Mei-Lan Tang, Stability analysis for
neutral systems with mixed delays, Journal of Computational and Applied
Mathematics, vol. 202 pp. 478-497, 2007.
[25] B. Wang, X. Liu, S. Zhong, New stability analysis for uncertain neutral
system with time-varying delay, Applied Mathematics and Computation,
vol. 197, pp. 457-465, 2008.
[1] S. Boyd, L.El. Ghaoui, E. Feron and V. Balakrishnan, Linear matrix
inequalities in systems and control theory. Philadelphia: SIAM 1994.
[2] J.K. Hale, S.M. & Verduyn Lunel, Introduction to functional differential
equation, New York: Springer 1993; 292-293.
[3] V. Kapila, W.M. Haddad, Memoryless H1 controllers for discrete time
systems with time delay, Automatica, vol. 35, pp. 1443-1451, 1998.
[4] J.X. Kuang, H.J. Tian, Taketomo Mitsui, Asymptotic and numerical
stability of systems of neutral differential equations with many delays.
Journal of Computational and Applied Mathematics, vol. 223, pp. 614-
625, 2009.
[5] H. Li, S.-M. Zhong, H.-b. Li, Some new simple stability criteria of linear
neutral systems with a single delay, Journal of Computational and Applied
Mathematics, vol. 200, pp. 441-447, 2007.
[6] S.Y. Xu, J. Lam, D.W.C. Ho,Y. Zou, Delay-dependent exponential
stability for a class of neural networks with time delays, Journal of
Computational and Applied Mathematics, vol. 183, pp. 16-28, 2005.
[7] C.-C. Shen, S.-M. Zhong, New delay-dependent robust stability criterion
for uncertain neutral systems with time-varying delay and nonlinear
uncertainties, Chaos, Solitons & Fractals vol. 40, pp. 2277-2285, 2009.
[8] Ji.F. Gao, H.Y. Su, X.F. Ji, J. Chu, Stability analysis for a class of neutral
systems with mixed delays and sector-bounded nonlinearity, Nonlinear
Analysis: Real World Applications, vol. 9, pp. 2350-2360, 2008.
[9] Ju.H. Park. Novel robust stability criterion for a class of neutral systems
with mixed delays and nonlinear perturbations. Applied Mathematics and
Computation, vol. 161, pp. 413-421, 2005.
[10] Q.-L. Han, On stability of linear neutral systems with mixed time delays:
A discretized Lyapunov functional approach, Automatica, vol. 41, pp.
1209-1218, 2005.
[11] Q.-L. Han, A descriptor system approach to robust stability of uncertain
neutral systems with discrete and distributed delays. IEEE Transactions
on Automatic Control, vol. 49, pp. 1791-1796, 2004.
[12] D.Y. Liu, X.Z. Liu, S.M. Zhong, Delay-dependent robust stability and
control synthesis for uncertain switched neutral systems with mixed
delays. Applied Mathematics and Computation, vol. 202, pp, 828-839,
2008.
[13] K.Q. Gu, S.I. Niculescu, Additional dynamics in transformed time-delay
systems, IEEE Trans. Autom. Control, vol. 45, pp. 572-575, 2000.
[14] Q.-L. Han, On robust stability of neutral systems with time-varying
discrete delay and norm-bounded uncertainty, IEEE Transactions on
Automatic Control, vol. 40, pp. 1087-1092, 2004.
[15] Z.R. Zhao, W. Wang, Bin Yang, Delay and its time-derivative dependent
robust stability of neutral control system, Applied Mathematics and
Computation, vol. 187, pp. 1326-1332, 2007.
[16] K. Wei, C.-H. Lie, Stability criteria for uncertain systems with interval
time-varying delays, Chaos, Solitons & Fractals, Available online vol. 38
pp. 650-657, 2008.
[17] O.M. Kwon, Ju.H. Park, S.M. Lee, On stability criteria for uncertain
delay-differential systems of neutral type with time-varying delays, Applied
Mathematics and Computation, vol. 197 pp. 864-873, 2008.
[18] J.-H. Kim, Delay and its time-derivative dependent robust stability
of time-delayed linear systems with uncertainty, IEEE Transactions on
Automatic Control, vol. 46 pp. 789-792, 2001.
[19] Y. He, M. Wu, Jin-Hua She, Guo-Ping Liu, Delay-dependent robust
stability criteria for uncertain neutral systems with mixed delays, Systems
& Control Letters, vol. 51 pp. 57-65, 2004.
[20] E. Fridman, U. Shaked, An improved approach stabilization method
for linear systems, IEEE Transactions on Automatic Control, vol. 47 pp.
1931-1937, 2002.
[21] M. Wu, Y. He, Jin-Hua She, Guo-Ping Liu, Delay-dependent criteria for
robust stability of time-varying delay systems, Automaticat, vol. 40 pp.
1435-1439, 2004.
[22] H.C. Yan, X.H. Huang, H. Zhang, M. Wang, Delay-dependent robust
stability criteria of uncertain stochastic systems with time-varying delay,
Chaos, Solitons & Fractals, vol. 40, pp. 1668-1679, 2009.
[23] Ju.H. Park, O. Kwon, On new stability criterion for delay-differential
systems of neutral type, Applied Mathematics and Computation, vol. 162;
pp. 627-637, 2005.
[24] X.-G. Liu, M. Wu, Ralph Martin, Mei-Lan Tang, Stability analysis for
neutral systems with mixed delays, Journal of Computational and Applied
Mathematics, vol. 202 pp. 478-497, 2007.
[25] B. Wang, X. Liu, S. Zhong, New stability analysis for uncertain neutral
system with time-varying delay, Applied Mathematics and Computation,
vol. 197, pp. 457-465, 2008.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:56441", author = "Changchun Shen and Shouming Zhong", title = "Improved Asymptotic Stability Criteria for Uncertain Neutral Systems with Time-varying Discrete Delays", abstract = "This paper investigates the robust stability of uncertain neutral system with time-varying delay. By using Lyapunov method and linear matrix inequality technology, new delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs), which can be easy to check the robust stability of the considered systems. Numerical examples are given to indicate significant improvements over some existing results.
", keywords = "Neutral system, linear matrix inequalities, Lyapunov, stability.", volume = "4", number = "1", pages = "69-6", }
