Improved delay-range-dependent stability criteria for linear systems with time-varying delays. (English) Zbl 1205.93139

Summary: This paper is concerned with the stability analysis of linear systems with time-varying delays in a given range. A new type of augmented Lyapunov functional is proposed which contains some triple-integral terms. In the proposed Lyapunov functional, the information on the lower bound of the delay is fully exploited. Some new stability criteria are derived in terms of linear matrix inequalities without introducing any free-weighting matrices. Numerical examples are given to illustrate the effectiveness of the proposed method.


93D30 Lyapunov and storage functions
93C05 Linear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
34H05 Control problems involving ordinary differential equations
Full Text: DOI


[1] Ariba, Y., & Gouaisbaut, F. (2007). Delay-dependent stability analysis of linear systems with time-varying delay. InProceedings of the 46th IEEE conference on decision and control (pp. 2053-2058) New Orleans, USA
[2] Fridman, E.; Shaked, U., Delay-dependent stability and \(\mathit{H}_\infty\) control: constant and time-varying delays, International journal of control, 76, 48-60, (2003) · Zbl 1023.93032
[3] Gao, H.; Wang, C., Comments and further results on “A descriptor system approach to \(\mathit{H}_\infty\) control of linear time-delay systems”, IEEE transactions on automatic control, 48, 520-525, (2003) · Zbl 1364.93211
[4] Gu, K. (2000). Integral inequality in the stability problem of time-delay systems. In Proceedings of the 39th IEEE conference on decision and control (pp. 2805-2810) Sydney, Australia
[5] Gu, K.; Kharitonov, V.-L.; Chen, J., Stability of time-delay systems, (2003), Brikhauser Boston · Zbl 1039.34067
[6] Hale, J.-K.; Verduyn Lunel, S.-M., ()
[7] Han, Q.-L., A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays, Automatica, 40, 1791-1796, (2004) · Zbl 1075.93032
[8] Han, Q.-L., On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty, Automatica, 40, 1087-1092, (2004) · Zbl 1073.93043
[9] Haoussi, F.E.; Tissir, E.H., Robust \(H_\infty\) controller design for uncertain neutral systems via dynamic observer based output feedback, International journal of automation and computing, 6, 164-170, (2009)
[10] He, Y.; Wang, Q.-G.; Lin, C.; Wu, M., Augmented Lyapunov functional and delay-dependent stability criteria for neutral systems, International journal of robust and nonlinear control, 15, 923-933, (2005) · Zbl 1124.34049
[11] He, Y.; Wang, Q.-G.; Xie, L.; Lin, C., Delay-range-dependent stability for systems with time-varying delay, Automatica, 43, 371-376, (2007) · Zbl 1111.93073
[12] He, Y.; Wu, M.; She, J.-H.; Liu, G.P., Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays, Systems & control letters, 51, 57-65, (2004) · Zbl 1157.93467
[13] Jiang, X.; Han, Q.-L., On \(\mathit{H}_\infty\) control for linear systems with interval time-varying delay, Automatica, 41, 2099-2106, (2005) · Zbl 1100.93017
[14] Kharitonov, V.-L.; Niculescu, S.-I., On the stability of linear systems with uncertain delay, IEEE transactions on automatic control, 48, 127-132, (2003) · Zbl 1364.34102
[15] Lin, C.; Wang, Q.-G.; Lee, H., A less conservative robust stability test for linear uncertain time-delay systems, IEEE transactions on automatic control, 51, 87-91, (2006) · Zbl 1366.93469
[16] Niculescu, S.-I., ()
[17] Niculescu, S.-I., On delay-dependent stability under model transformations of some neutral linear systems, International journal of control, 74, 609-617, (2001) · Zbl 1047.34088
[18] Park, P., A delay-dependent stability criterion for systems with uncertain time-invariant delays, IEEE transactions on automatic control, 44, 876-877, (1999) · Zbl 0957.34069
[19] Shao, H.-Y., New delay-dependent stability criteria for systems with interval delay, Automatica, 45, 744-749, (2009) · Zbl 1168.93387
[20] Sun, J.; Liu, G.-P.; Chen, J., Delay-dependent stability and stabilization of neutral time-delay systems, International journal of robust and nonlinear control, 19, 1364-1375, (2009) · Zbl 1169.93399
[21] Suplin, V.; Fridman, E.; Shaked, U., \(H_\infty\) control of linear uncertain time-delay systems — a projection approach, IEEE transactions on automatic control, 51, 680-685, (2006) · Zbl 1366.93163
[22] Xu, S.; Lam, J., Improved delay-dependent stability criteria for time-delay systems, IEEE transactions on automatic control, 50, 384-387, (2005) · Zbl 1365.93376
[23] Yue, D.; Han, Q.-L.; Lam, J., Network-based robust \(H_\infty\) control of systems with uncertainty, Automatica, 41, 999-1007, (2005) · Zbl 1091.93007
[24] Zhang, Y.; Wu, A.-G.; Duan, G.-R., Enhanced \(H_\infty\) filtering for continuous-time state-delayed systems, International journal of automation and computing, 6, 159-163, (2009)
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