Li, Shukai; Tang, Wansheng; Zhang, Jianxiong Guaranteed cost control of synchronisation for uncertain complex delayed networks. (English) Zbl 1259.93088 Int. J. Syst. Sci. 43, No. 3, 566-575 (2012). Summary: The synchronisation for a class of complex delayed dynamical networks with uncertain inner coupling configuration is investigated under the quadratic guaranteed cost control. The coupling delay and nodes delay are considered in the networks. Based on Lyapunov–Krasovskii stability theory, sufficient conditions for the existence of the optimal guaranteed cost control laws are given in terms of linear matrix inequalities. Under these sufficient conditions, the networks are globally asymptotically synchronous, and the optimal upper bound is also guaranteed. Numerical examples are given to illustrate the effectiveness of the proposed methods. Cited in 12 Documents MSC: 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory 49N90 Applications of optimal control and differential games 93C15 Control/observation systems governed by ordinary differential equations Keywords:synchronisation; guaranteed cost control; time delays; uncertainty; linear matrix inequalities PDFBibTeX XMLCite \textit{S. Li} et al., Int. J. Syst. Sci. 43, No. 3, 566--575 (2012; Zbl 1259.93088) Full Text: DOI References: [1] DOI: 10.1103/RevModPhys.74.47 · Zbl 1205.82086 · doi:10.1103/RevModPhys.74.47 [2] DOI: 10.1103/PhysRevLett.89.054101 · doi:10.1103/PhysRevLett.89.054101 [3] Boyd S, Linear Matrix Inequalities in System and Control Theory (1994) · Zbl 0816.93004 · doi:10.1137/1.9781611970777 [4] DOI: 10.1109/TAC.1972.1100037 · Zbl 0259.93018 · doi:10.1109/TAC.1972.1100037 [5] DOI: 10.1080/00207720802645261 · Zbl 1291.93021 · doi:10.1080/00207720802645261 [6] DOI: 10.1016/j.physa.2004.05.058 · doi:10.1016/j.physa.2004.05.058 [7] DOI: 10.1016/j.physleta.2004.02.058 · Zbl 1123.93316 · doi:10.1016/j.physleta.2004.02.058 [8] DOI: 10.1016/j.physleta.2008.10.054 · Zbl 1226.05232 · doi:10.1016/j.physleta.2008.10.054 [9] DOI: 10.1016/j.physleta.2007.10.020 · Zbl 1217.05210 · doi:10.1016/j.physleta.2007.10.020 [10] DOI: 10.1007/s11071-007-9299-x · Zbl 1182.92007 · doi:10.1007/s11071-007-9299-x [11] DOI: 10.1080/00207720802645238 · Zbl 1291.93015 · doi:10.1080/00207720802645238 [12] DOI: 10.1016/j.chaos.2005.04.076 · Zbl 1102.37305 · doi:10.1016/j.chaos.2005.04.076 [13] Ren HP, Acta Physica Sinica – Chinese Edition 55 pp 2694– (2006) [14] DOI: 10.1038/35065725 · Zbl 1370.90052 · doi:10.1038/35065725 [15] DOI: 10.1016/j.physa.2007.03.011 · doi:10.1016/j.physa.2007.03.011 [16] DOI: 10.1142/S0218127402004802 · Zbl 1044.37561 · doi:10.1142/S0218127402004802 [17] DOI: 10.1142/S0218127402004292 · doi:10.1142/S0218127402004292 [18] Wang XF, Journal of Systems Science and Complexity 16 pp 358– (2003) [19] DOI: 10.1080/00207720903237471 · Zbl 1298.00189 · doi:10.1080/00207720903237471 [20] DOI: 10.1016/j.physa.2006.12.037 · doi:10.1016/j.physa.2006.12.037 [21] DOI: 10.1080/00207179608921866 · Zbl 0841.93014 · doi:10.1080/00207179608921866 [22] DOI: 10.1016/j.chaos.2009.03.158 · Zbl 1198.93023 · doi:10.1016/j.chaos.2009.03.158 [23] DOI: 10.1002/rnc.1339 · Zbl 1160.93342 · doi:10.1002/rnc.1339 [24] DOI: 10.1016/j.physa.2007.07.006 · doi:10.1016/j.physa.2007.07.006 [25] DOI: 10.1007/s10957-008-9411-5 · Zbl 1152.93029 · doi:10.1007/s10957-008-9411-5 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.