Improved Asymptotic Stability Analysis for Lure Systems with Neutral Type and Time-varying Delays

Authors: Changchun Shen, Shouming Zhong

Abstract:

This paper investigates the problem of absolute stability and robust stability of a class of Lur-e systems with neutral type and time-varying delays. By using Lyapunov direct method and linear matrix inequality technique, new delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs) which are easy to check the stability of the considered systems. To obtain less conservative stability conditions, an operator is defined to construct the Lyapunov functional. Also, the free weighting matrices approach combining a matrix inequality technique is used to reduce the entailed conservativeness. Numerical examples are given to indicate significant improvements over some existing results.

Keywords: Lur'e system, linear matrix inequalities, Lyapunov, stability.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1078949

References:

[1] J. K. Hale, S. M. & Verduyn Lunel Introduction to functional differential equation. New York: Springer 1993:292-293
[2] S. Boyd, L.El. Ghaoui, E. Feron, &V. Balakrishnan, Linear matrix inequalities in systems and control theory. Philadelphia: SIAM 1994.
[3] H. Miyagi, K. Yamashita, Stability studies of control systems using a non-Lur-e type Lyapunov function. IEEE Trans. Automat. Control 1986;31:970-972.
[4] T. Li, J.J. Yu, Z. Wang, Delay-range-dependent synchronization criterion for Lure systems with delay feedback control. Communications in Nonlinear Science and Numerical Simulation 2009;14;1796-1803.
[5] S.M. Lee, Ju H. Park, Delay-dependent criteriaforabsolutestabilityof uncertain time-delayedLuredynamicalsystems. Journal of the Franklin Institute 2010;347:146-153.
[6] Q.-L. Han, A new delay-dependent absolute stability criterion for a class of nonlinear neutral systems. Automatica 2008;44:272-277.
[7] S. M. Lee, O. M. Kwon, Ju H. Park, Novel robust delay dependent criterion for absloute stability of Lur-e of neutral type. Modern Physics Letters B (MPLB) 2009;23:1641-1650.
[8] Y. He, M. Wu, Absolute stability for multiple delay general Lur-e control systems with multiple nonlinearities. Journal of Computational and Applied Mathematics 2003;159:241-248.
[9] Y. He, M. Wu, J.-H. She, Guo-Ping Liu, Robust stability for delay Lur-e control systems with multiple nonlinearities. Journal of Computational and Applied Mathematics 2005;176:371-380.
[10] J.F. Gao, H.Y. Su, Xiaofu Ji, Jian Chu, Stability analysis for a class of neutral systems with mixed delays and sector-bounded nonlinearity. Nonlinear Analysis: Real World Applications 2008;9:2350-2360.
[11] S.J. Choi, S.M. Lee, S.C. Won, Ju H. Park, Improved delay-dependent stability criteria for uncertain Lur-e systems with sector and slope restricted nonlinearities and time-varying delays. Applied Mathematics and Computation 2009;208:520-530.
[12] K. Gu, V.L. Kharitonov, J. Chen, Stability of Time-Delay Systems. Birkhauser, Boston, 2003.
[13] K.Q. Gu, S.I. Niculescu, Additional dynamics in transformed time-delay systems. IEEE Trans. Autom. Control 2000;45:572-575.
[14] 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 2008;202:828-839.
[15] J.H. Park, Novel robust stability criterion for a class of neutral systems with mixed delays and nonlinear perturbations. Appl. Math. Comput. 2005;161;413-421.
[16] W.-H. Chen, W. X. Zheng. Delay-dependent robust stabilization for uncertain neutral systems with distributed delays. Automatica 2007;43:95- 104.
[17] X.H. Nian, Delay dependent conditions for absolute stability of Lurie type control systems. Acta Automatica Sin. 1999;25:564-566.
[18] B. Yang, J.C. Wang, Delay-dependent criterion for absolute stability of neutral general lurie systems, Acta Automatica Sin. 2004;30:261-264.
[19] L. Yu, Q.L. Han, S.M. Yu, J.F. Gao, Delay-dependent conditions for robust absolute stability of uncertain time-delay systems. Proceedings of the 42nd IEEE Conference on Decision and Control 2003:6033-6037.
[20] Q.L. Han, Absolute stability of time-delay systems with sector-bounded nonlinearity. Automatica 2005;41:2171-2176.
[21] F. Qiu, B.T. Cui, Y. Ji, Novel robust stability analysis for uncertain neutral system with mixed delays, Chaos, Solitons and Fractals 42 (2009) 1820-1828 .
[22] L.L. Xiong, S.M. Zhong, J.K. Tian, Novel robust stability criteria of uncertain neutral systems with discrete and distributed delays, Chaos, Solitons and Fractals 40 (2009) 771-777.