New Delay-dependent Stability Conditions for Neutral Systems with Nonlinear Perturbations
In this paper, the problem of asymptotical stability of neutral systems with nonlinear perturbations is investigated. Based on a class of novel augment Lyapunov functionals which contain freeweighting matrices, some new delay-dependent asymptotical stability criteria are formulated in terms of linear matrix inequalities (LMIs) by using new inequality analysis technique. Numerical examples are given to demonstrate the derived condition are much less conservative than those given in the literature.
[1] Y.-Y. Cao, J. Lam, Computation of robust stability bounds for time-delay
systems with nonlinear time-varying perturbation, International Journal
of Systems Science, Vol. 31, No. 3, pp. 359-365, 2000.
[2] Y. Chen, A.-K. Xue, R.-Q. Lu, S.-S. Zhou, On robustly exponential
stability of uncertain neutral systems with time-varying delays and
nonlinearperturbations, Nonlinear Analysis: Theory, Methods & Applications,
Vol. 68, No. 8, pp. 2464-2470, 2008.
[3] K.-Q. Gu, A further refinement of discretized Lyapunov functional
method for the stability of time-delay systems, International Journal of
control, Vol. 74, No. 10, pp. 967-976, 2001.
[4] Q.-L. Han, Robust stability for a class of linear systems with time-varying
delay and nonlinear perturbations, Computer and Mathematics with
Applications,Vol. 47, No. 8-9, pp. 1201-1209, 2004.
[5] Q.-L. Han, On robust stability of linear neutral systems with nonlinear
parameter perturbations, Proceeding of the 2004 American Control
Conference, Boston, Massachusetts, June 30-July 2, pp. 2027-2032, 2004.
[6] Q.-L. Han, L. Yu, Robust stability of linear neutral systems with nonlinear
parameter perturbations, IEE Proceedings Control Theory &
Applications, Vol. 151, No. 5, pp. 539-546, 2004.
[7] Q.-L. Han, On stability of linear neutral systems with mixed time delays:
A discretized Lyapunov functional approach, Automatica,Vol. 41, No.
7, pp. 1209-1218, 2005.
[8] Y. He, Q.-G. Wang, C. Lin, M. Wu, Augmented Lyapunov functional
and delay dependent stability criteria for neutral systems, International
Journal of Robust and Nonlinear Control, Vol. 15, No. 18, pp. 923-933,
2005.
[9] Jack K. Hale, Sjoerd M. Verduyn Lunel, Introduction to Functional
Differential Equations, Applied Mathematical Sciences, Springer: New
York, 1993.
[10] H. Li, H.-B. Li, S.-M. Zhong, Some new simple stability criteria of
linear neutral systems with a single delay, Journal of Computational
and Applied Mathematics, Vol. 200, No. 1, pp. 441-447, 2007.
[11] D.-Y. Liu, S.-M. Zhong, L.-L. Xiong, On robust stability of uncertain
neutral systems with multiple delays, Chaos, Solitons & Fractals, Vol.
39, No. 5, pp. 2332-2339, 2009.
[12] X.-G. Liu, M. Wu, Ralph Martin, M.-L. Tang, Stability analysis for
neutral systems with mixed delays, Journal of Computational and
Applied Mathematics, Vol. 202, No. 2, pp. 478-497, 2007.
[13] Nakano M, Hara S. In Microprocessor-based Repetitive Control,
Microprocessor-Based Control Systems, Sinha NK (ed.). D. Reidel Publishing
Company: Dordrecht, 1986.
[14] J.-H. Park, Novel robust stability criterion for a class of neutral systems
with mixed delays and nonlinear perturbations. Applied Mathematics
and Computation, Vol. 161, No. 2, pp. 413-421, 2005.
[15] Stephen Boyd, Laurent El Ghaoui, Eric Feron, Venkataramanan Balakrishnan,
Linear matrix inequalities in systems and control theory.
Philadelphia: SIAM, 1994.
[16] Marshall Slemrod, E.-F. Infante , Asymptotic stability criteria for linear
systems of differential equations of neutral type and their discrete
analogues, Journal of Mathematical Analysis and Application, Vol.
38, No. 2, pp. 399-415, 1972.
[17] L.-L. Xiong, S.-M. Zhong, J.-K. Tian, Novel robust stability criteria of
uncertain neutral systems with discrete and distributed delays. Chaos,
Solitons & Fractals, Vol. 40, No. 2, pp. 771-777, 2009.
[18] Y. Kuang. Delay Differential Equations with Applications in Population
Dynamics. Academic Press: Boston, 1993.
[19] V.-A. Yakubovich, S-procedure in nonlinear control theory, Vestnik.
Leningradskogo Universiteta, Ser. Matematika, Vol. 1, No. 13, pp.
62-77, 1971.
[20] L.-L Xiong, S.-M. Zhong, D.-Y. Li, Novel delay-dependent asymptotical
stability of neutral systems with nonlinear perturbations, Journal of
Computational and Applied Mathematics, Vol. 232, No. 2, pp. 505-513,
2009.
[21] W.-A. Zhang, L. Yu. Delay-dependent Robust Stability of Neutral Systems
with Mixed Delays and Nonlinear Perturbations, Acta Automatica
Sinica, Vol. 33, No. 8, pp. 863-866, 2007.
[22] X.-M. Zhang, Study on Delay-dependent Robust Control Based on An
Integral Inequality Approach, PhD thesis, School of Information Science
and Engineering, Central South University, 2006.
[23] Z. Zou, Y. Wang, New stability criterion for a class of linear systems
with time-varying delay and nonlinear perturbations, IEE Proceedings
Control Theory and Applications, Vol. 153, No. 5, pp. 623-626, 2006.
[1] Y.-Y. Cao, J. Lam, Computation of robust stability bounds for time-delay
systems with nonlinear time-varying perturbation, International Journal
of Systems Science, Vol. 31, No. 3, pp. 359-365, 2000.
[2] Y. Chen, A.-K. Xue, R.-Q. Lu, S.-S. Zhou, On robustly exponential
stability of uncertain neutral systems with time-varying delays and
nonlinearperturbations, Nonlinear Analysis: Theory, Methods & Applications,
Vol. 68, No. 8, pp. 2464-2470, 2008.
[3] K.-Q. Gu, A further refinement of discretized Lyapunov functional
method for the stability of time-delay systems, International Journal of
control, Vol. 74, No. 10, pp. 967-976, 2001.
[4] Q.-L. Han, Robust stability for a class of linear systems with time-varying
delay and nonlinear perturbations, Computer and Mathematics with
Applications,Vol. 47, No. 8-9, pp. 1201-1209, 2004.
[5] Q.-L. Han, On robust stability of linear neutral systems with nonlinear
parameter perturbations, Proceeding of the 2004 American Control
Conference, Boston, Massachusetts, June 30-July 2, pp. 2027-2032, 2004.
[6] Q.-L. Han, L. Yu, Robust stability of linear neutral systems with nonlinear
parameter perturbations, IEE Proceedings Control Theory &
Applications, Vol. 151, No. 5, pp. 539-546, 2004.
[7] Q.-L. Han, On stability of linear neutral systems with mixed time delays:
A discretized Lyapunov functional approach, Automatica,Vol. 41, No.
7, pp. 1209-1218, 2005.
[8] Y. He, Q.-G. Wang, C. Lin, M. Wu, Augmented Lyapunov functional
and delay dependent stability criteria for neutral systems, International
Journal of Robust and Nonlinear Control, Vol. 15, No. 18, pp. 923-933,
2005.
[9] Jack K. Hale, Sjoerd M. Verduyn Lunel, Introduction to Functional
Differential Equations, Applied Mathematical Sciences, Springer: New
York, 1993.
[10] H. Li, H.-B. Li, S.-M. Zhong, Some new simple stability criteria of
linear neutral systems with a single delay, Journal of Computational
and Applied Mathematics, Vol. 200, No. 1, pp. 441-447, 2007.
[11] D.-Y. Liu, S.-M. Zhong, L.-L. Xiong, On robust stability of uncertain
neutral systems with multiple delays, Chaos, Solitons & Fractals, Vol.
39, No. 5, pp. 2332-2339, 2009.
[12] X.-G. Liu, M. Wu, Ralph Martin, M.-L. Tang, Stability analysis for
neutral systems with mixed delays, Journal of Computational and
Applied Mathematics, Vol. 202, No. 2, pp. 478-497, 2007.
[13] Nakano M, Hara S. In Microprocessor-based Repetitive Control,
Microprocessor-Based Control Systems, Sinha NK (ed.). D. Reidel Publishing
Company: Dordrecht, 1986.
[14] J.-H. Park, Novel robust stability criterion for a class of neutral systems
with mixed delays and nonlinear perturbations. Applied Mathematics
and Computation, Vol. 161, No. 2, pp. 413-421, 2005.
[15] Stephen Boyd, Laurent El Ghaoui, Eric Feron, Venkataramanan Balakrishnan,
Linear matrix inequalities in systems and control theory.
Philadelphia: SIAM, 1994.
[16] Marshall Slemrod, E.-F. Infante , Asymptotic stability criteria for linear
systems of differential equations of neutral type and their discrete
analogues, Journal of Mathematical Analysis and Application, Vol.
38, No. 2, pp. 399-415, 1972.
[17] L.-L. Xiong, S.-M. Zhong, J.-K. Tian, Novel robust stability criteria of
uncertain neutral systems with discrete and distributed delays. Chaos,
Solitons & Fractals, Vol. 40, No. 2, pp. 771-777, 2009.
[18] Y. Kuang. Delay Differential Equations with Applications in Population
Dynamics. Academic Press: Boston, 1993.
[19] V.-A. Yakubovich, S-procedure in nonlinear control theory, Vestnik.
Leningradskogo Universiteta, Ser. Matematika, Vol. 1, No. 13, pp.
62-77, 1971.
[20] L.-L Xiong, S.-M. Zhong, D.-Y. Li, Novel delay-dependent asymptotical
stability of neutral systems with nonlinear perturbations, Journal of
Computational and Applied Mathematics, Vol. 232, No. 2, pp. 505-513,
2009.
[21] W.-A. Zhang, L. Yu. Delay-dependent Robust Stability of Neutral Systems
with Mixed Delays and Nonlinear Perturbations, Acta Automatica
Sinica, Vol. 33, No. 8, pp. 863-866, 2007.
[22] X.-M. Zhang, Study on Delay-dependent Robust Control Based on An
Integral Inequality Approach, PhD thesis, School of Information Science
and Engineering, Central South University, 2006.
[23] Z. Zou, Y. Wang, New stability criterion for a class of linear systems
with time-varying delay and nonlinear perturbations, IEE Proceedings
Control Theory and Applications, Vol. 153, No. 5, pp. 623-626, 2006.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59897", author = "Lianglin Xiong and Xiuyong Ding and Shouming Zhong", title = "New Delay-dependent Stability Conditions for Neutral Systems with Nonlinear Perturbations", abstract = "In this paper, the problem of asymptotical stability of neutral systems with nonlinear perturbations is investigated. Based on a class of novel augment Lyapunov functionals which contain freeweighting matrices, some new delay-dependent asymptotical stability criteria are formulated in terms of linear matrix inequalities (LMIs) by using new inequality analysis technique. Numerical examples are given to demonstrate the derived condition are much less conservative than those given in the literature.
", keywords = "Asymptotical stability, neutral system, nonlinear perturbation, delay-dependent, linear matrix inequality (LMI).", volume = "4", number = "7", pages = "960-7", }
