Improved Robust Stability Criteria of a Class of Neutral Lur’e Systems with Interval Time-Varying Delays
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.
<p>[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.</p>
<p>[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.</p>
@article{"International Journal of Engineering, Mathematical and Physical Sciences:65398", author = "Longqiao Zhou and Zixin Liu and Shu Lü", title = "Improved Robust Stability Criteria of a Class of Neutral Lur’e Systems with Interval Time-Varying Delays", 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.", volume = "7", number = "5", pages = "917-8", }
