Improved Asymptotic Stability Analysis for Lure Systems with Neutral Type and Time-varying Delays
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:61334", author = "Changchun Shen and Shouming Zhong", title = "Improved Asymptotic Stability Analysis for Lure Systems with Neutral Type and Time-varying Delays", 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.", volume = "4", number = "1", pages = "131-7", }
