Improved Robust Stability Criteria of a Class of Neutral Lur’e Systems with Interval Time-Varying Delays
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33122
Improved Robust Stability Criteria of a Class of Neutral Lur’e Systems with Interval Time-Varying Delays

Authors: Longqiao Zhou, Zixin Liu, Shu Lü

Abstract:

This paper addresses the robust stability problem of a class of delayed neutral Lur’e systems. Combined with the property of convex function and double integral Jensen inequality, a new tripe integral Lyapunov functional is constructed to derive some new stability criteria. Compared with some related results, the new criteria established in this paper are less conservative. Finally, two numerical examples are presented to illustrate the validity of the main results.

Keywords: Lur’e system, Convex function, Jensen integral inequality, Triple-integral method, Exponential stability.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1088368

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1519

References:


[1] A.I. Lur’e, Some nonliear problem in the theory of automatic control, H.M. Stationary Office, London, 1975.
[2] X. Nian,Delay dependent conditions for absolute stability of Lur’e type control systems, Acta Automat. Sinica 25 (1999) 556-564 B.J.
[3] B. Xu, X. Liao, Absolute stability criteria of delay-dependent for Lur’e control systems, Acta Automat. Sinica 28 (2002) 317-320.
[4] Y. He, M. Wu, Absolute stability for multiple delay general Lur’e control systems with multiple nonlinearities, J. Comput. Appl. Math. 159 (2003) 241-248.
[5] D. Chen, W. Liu, Delay-dependent robust stability for Lur’e control systems with multiple time delays, Contr. Theor. Appl. 22 (2005) 499- 502.
[6] J. Cao , S.M. Zhong, New delay-dependent condition for absolute stability of Lurie control systems with multiple time-delays and nonlinearities, Appl. Math. Comput. 194 (2007) 250-258.
[7] J. Cao , S.M. Zhong, Y.Y. Hu, Delay-dependent condition for absolute stabilityof Lur’e control systems with multiple time delays and nonlinearities, J. Math. Anal. Appl. 338 (2008) 497-504.
[8] V.A. Yakubovich, G.A. Leonov, A.Kh. Gelig, Stability of Stationary Sets in Control Systems with Discontinuous Nonlinearities, World Scientific, Singapore, 2004.
[9] P.A. Bliman, Lyapunov-Krasovskii functionals and frequency domain: Delay-independent absolute stability criteria for delay systems,Internat. J. Robust Nonlinear Control 11 (2001) 771-788.
[10] F.O. Souza, R.M. Pallhares, E.M.A.M. Mendes, L.A.B Torres, control for master-slave synchronization of Lur’e systems with time-varying feedback control, Int. J. Bifur. Chaos, 18(4) (2008) 1161-1173.
[11] O. Mason, R. Shorten, A conjecture on the existence of common quadratic Lyapunov functions for positive linear systems, in: Proc. Ameri. Contr. Conf., 2003.
[12] L. Gurvits, R. Shorten, O. Mason, On the stability of switched positive linear systems, IEEE Trans. Automat. Control, 52 (6)(2007) 1099-1103.
[13] J.G Park, A delay-dependent stability criterion for systems with uncertain linear state-delayed systems, IEEE Trans. Autom. Control 35 (1999) 878-877.
[14] E. Fridman, U. Shaked, control of linear state-delay descriptor systems: an LMI approach, Linear Algebra and its Applications 351-352 (2002) 271-302.
[15] F.O. Souza, R.M Palhares, V.J.S. Leite, Improved robust control for neutral systems via discretied Lyapunov-Krasovskii functional, Int. J. Control, 81(9)(2008) 1462-1474.
[16] K. Yu, C. Lien, Stability criteria for uncertain neutral systems with interval time-verying delays, Chaos, Solition and Fractals, 38 (2008) 650-657.
[17] Chun Yin, Shou-ming Zhong, and Wu-fan Chen, On delay-dependent robust stability of a class of uncertain mixed neutral and Lur’e dynamical systems with interval time-varying delays, Journal of the Franklin Institute, 347(9)(2010) 1623-1642.
[18] J. Sun, G.P. Liu, J. Chen, ’Delay-dependent stability and stabilization of neutral time-delay systems, Int. J. Roubst Nonlinear Control. 19 (2009) 1364-1375.
[19] J.H. Park , O.M. Kwon , S.M. Lee, LMI optimization approach on stability for delayed neural networks of neutral-type,Appl. Math. Comput. 196 (2008) 236-244.
[20] J. Sun, G.P. Liu, J. Chen, D. Ree, Networked Predictive Control for neural networks with time-varying interval delay. Phys. Lett. A. 373 (2009) 342-348.
[21] J. Cao, H Sun, X.F. Ji, J. Chu, Stability analysis for a class of neutral systems with mixed delays and sector-bounded nonlinearity. Nonlinearity Analysis, Real World Appl. 9 (2008) 2350-2360.
[22] S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnam, SIMA, Philadelphia, 1994.