Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30172
New Delay-dependent Stability Conditions for Neutral Systems with Nonlinear Perturbations

Authors: Lianglin Xiong, Xiuyong Ding, Shouming Zhong

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).

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1076026

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1115

References:


[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.