Improved delay-dependent bounded real lemma for uncertain time-delay systems. (English) Zbl 1171.93333

Summary: This paper concerns reducing the conservatism of delay-dependent Bounded Real Lemma (BRL) of time-delay systems with uncertainty described by a linear fractional form. By introducing an augmented Lyapunov functional, an improved BRL is established in terms of Linear Matrix Inequalities (LMIs). Theoretical comparisons show that the obtained BRL is less conservative than some previous ones and the recent results in [S. Xu, J. Lam and Y. Zou, Automatica 42, No. 2, 343–348 (2006; Zbl 1099.93010); T. Li, L. Guo, C. Lin and Y. M. Zhang, Delay-range-dependent bounded real lemma for time-delay systems, Asian J. Control 10, 708–717 (2008)] are actually equivalent to the special cases of the obtained BRL. Numerical examples are also given to demonstrate the effectiveness of the proposed result.


93C05 Linear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
93B35 Sensitivity (robustness)
93C41 Control/observation systems with incomplete information


Zbl 1099.93010
Full Text: DOI


[1] Choi, H. H.; Chung, M. J., An LMI approach to \(H_\infty\) controller design for linear time-delay systems, Automatica, 33, 737-739 (1997) · Zbl 0875.93104
[2] Curtain, R. F., The strict bounded real lemma in infinite dimensions, Systems Control Letter, 20, 113-116 (1993) · Zbl 0782.93043
[3] Fridman, E.; Shaked, U., A descriptor system approach to \(H_\infty\) control of linear time-delay systems, IEEE Transactions on Automatic Control, 47, 253-270 (2002) · Zbl 1364.93209
[4] Gao, H.; Wang, C., Comments and further results on A descriptor system approach to \(H_\infty\) control of linear time-delay systems, IEEE Transactions on Automatic Control, 48, 520-525 (2003) · Zbl 1364.93211
[6] Guo, L., \(H_\infty\) output feedback control for delay systems with nonlinear and parametric uncertainties, IEE Proceedings Control Theory Application, 149, 226-236 (2002)
[7] Lee, Y. S.; Moon, Y. S.; Kwon, W. H.; Park, P. G., Delay-dependent robust \(H_\infty\) control for uncertain systems with a state-delay, Automatica, 40, 65-72 (2004) · Zbl 1046.93015
[8] Skelton, R. E.; Iwasaki, T.; Grigoriadis, K., A Unified Algebraic Approach to Linear Control Design (1998), Taylor and Francis: Taylor and Francis Bristol, PA
[9] Zhou, S. S.; Lam, J., Robust stabilization of delayed singular systems with linear fractional parametric uncertainties, Circuits System Signal Process, 22, 579C588 (2003)
[10] Xu, S. Y.; James, L.; Zou, Y., New results on delay-dependent robust \(H_\infty\) control for systems with time-varying delays, Automatica, 42, 343-348 (2006) · Zbl 1099.93010
[11] Gao, H.; Chen, T. W.; James, L., A new delay system approach to network-based control, Automatica, 44, 39-52 (2008) · Zbl 1138.93375
[12] Li, T.; Guo, L.; Lin, C.; Zhang, Y. M., Delay-range-dependent bounded real lemma for time delay systems, Asian Journal of Control, 10, 708-717 (2008)
[13] He, Y.; Wang, Q. G.; Xie, L. H.; Lin, C., Further improvement of free-weighting matrices technique for systems with time-varying delay, IEEE Transactions on Automatic Control, 52, 293-299 (2007) · Zbl 1366.34097
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