Chen, Yonggang; Bi, Weiping; Li, Wenlin New delay-dependent absolute stability criteria for Lur’e systems with time-varying delay. (English) Zbl 1235.34193 Int. J. Syst. Sci. 42, No. 7, 1105-1113 (2011). Summary: The absolute stability problem is investigated for Lur’e systems with time-varying delay and sector-bounded nonlinearity. By employing the idea of delay fractioning, a new augmented Lyapunov functional is constructed first. Then, by introducing some slack matrices and by reserving the useful term when estimating the upper bound of the derivative of the Lyapunov functional, new delay-dependent absolute stability criteria are derived in terms of linear matrix inequalities. Several numerical examples are presented to show the effectiveness and the less-conservativeness of the proposed method. Cited in 9 Documents MSC: 34K20 Stability theory of functional-differential equations Keywords:absolute stability; Lur’e systems; time-varying delay; linear matrix inequalities PDFBibTeX XMLCite \textit{Y. Chen} et al., Int. J. Syst. Sci. 42, No. 7, 1105--1113 (2011; Zbl 1235.34193) Full Text: DOI References: [1] DOI: 10.1080/002071700445370 · Zbl 1002.93048 [2] DOI: 10.1109/TAC.2002.804462 · Zbl 1364.93564 [3] DOI: 10.1080/0020717021000049151 · Zbl 1023.93032 [4] DOI: 10.1006/jmaa.2001.7433 · Zbl 0995.93041 [5] DOI: 10.1016/j.nonrwa.2007.07.003 · Zbl 1156.34345 [6] DOI: 10.1007/978-1-4612-0039-0 [7] Hale JK, Introduction to Functional Differential Equations (1993) [8] DOI: 10.1016/j.automatica.2005.08.005 · Zbl 1100.93519 [9] DOI: 10.1016/j.physleta.2006.08.076 · Zbl 1236.93072 [10] DOI: 10.1049/iet-cta:20060213 [11] DOI: 10.1016/S0377-0427(03)00457-6 · Zbl 1032.93062 [12] DOI: 10.1016/S0167-6911(03)00207-X · Zbl 1157.93467 [13] DOI: 10.1109/TAC.2004.828317 · Zbl 1365.93368 [14] DOI: 10.1002/rnc.1039 · Zbl 1124.34049 [15] DOI: 10.1016/j.cam.2004.07.025 · Zbl 1076.93036 [16] DOI: 10.1109/TAC.2006.887907 · Zbl 1366.34097 [17] Khalil HK, Nonlinear Systems (1996) [18] Lur’e AI, On Some Nonlinear Problems in the Theory of Automatic Control (1957) [19] Mahmoud MS, Resilient Control of Uncertain Dynamical Systems (2004) · Zbl 1103.93003 [20] DOI: 10.1080/00207170110067116 · Zbl 1023.93055 [21] DOI: 10.1080/00207729808929511 [22] DOI: 10.1080/002077299291723 · Zbl 1033.93507 [23] DOI: 10.1016/j.physleta.2006.06.068 [24] DOI: 10.1049/iet-cta:20060539 [25] DOI: 10.1142/S021812740100295X [26] DOI: 10.1080/00207720701433033 · Zbl 1128.93017 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.