×

Global synchronised regions of linearly coupled Lur’e systems. (English) Zbl 1222.93085

Summary: This article addresses the global synchronisation problem of a network of coupled Lur’e systems from the perspective of global synchronised region. A decomposition approach is proposed to convert the synchronisation of high-dimensional Lur’e networks into the test of a set of matrix inequalities whose dimensions are the same as a single Lur’e node. The notion of global synchronised region is then introduced and analysed. A necessary and sufficient condition is derived for the existence of the inner-linking matrix to guarantee a desirable unbounded synchronised region. A multi-step design procedure is given for constructing such an inner-linking matrix, which maintains a favourable decoupling property. Furthermore, the global \(H _{\infty }\) synchronised region is characterised for evaluating the performance of a Lur’e network subject to external disturbances. The effectiveness of the theoretical results is demonstrated through a network of Chua’s circuits.

MSC:

93B52 Feedback control
93B36 \(H^\infty\)-control
93C05 Linear systems in control theory

Software:

YALMIP
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] DOI: 10.1103/PhysRevLett.89.054101
[2] Boyd S, Linear Matrix Inequalities in Systems and Control Theory (1994) · Zbl 0816.93004
[3] DOI: 10.1109/TCSI.2007.895383 · Zbl 1374.93297
[4] DOI: 10.1103/PhysRevE.76.056103
[5] DOI: 10.1016/j.physleta.2008.02.056 · Zbl 1220.34074
[6] DOI: 10.1109/TAC.2008.2009690 · Zbl 1367.93461
[7] DOI: 10.1080/00207170903062182 · Zbl 1178.93014
[8] Horn R, Matrix Analysis (1985) · Zbl 0576.15001
[9] DOI: 10.1063/1.2959852 · Zbl 1309.34095
[10] DOI: 10.1016/0005-1098(94)90110-4 · Zbl 0806.93017
[11] DOI: 10.1016/j.physleta.2009.01.038 · Zbl 1228.34076
[12] Khalil HK, Nonlinear Systems,,, 3. ed. (2002)
[13] DOI: 10.1109/TCSI.2004.835655 · Zbl 1374.94915
[14] DOI: 10.1109/TCSI.2010.2043018
[15] Li, ZK, Duan, ZS and Huang, L. 2007. Global Synchronization of Complex Lur’e Networks. Proceedings of the Chinese Control Conference. 2007. pp.304–308. Zhangjiajie, China
[16] DOI: 10.1016/j.physa.2007.08.006
[17] Löfberg J, Proceedings of IEEE International Symposium on Computer-Aided Control System Design pp 284– (2004)
[18] DOI: 10.1109/TCSII.2007.916788
[19] DOI: 10.1016/S0024-3795(97)10080-5 · Zbl 0932.05057
[20] Ogata K, Modern Control Engineering,,, 3. ed. (1996)
[21] DOI: 10.1080/002071797223479 · Zbl 0896.93024
[22] DOI: 10.1103/PhysRevLett.80.2109
[23] DOI: 10.1016/0167-6911(95)00063-1 · Zbl 0866.93052
[24] DOI: 10.1109/TAC.2005.846556 · Zbl 1365.93302
[25] DOI: 10.1103/PhysRevE.75.046103
[26] DOI: 10.1103/PhysRevE.75.016210
[27] DOI: 10.1080/10556789908805766 · Zbl 0973.90526
[28] DOI: 10.1142/S0218127497000467 · Zbl 0925.93343
[29] DOI: 10.1109/81.774230 · Zbl 1055.93549
[30] DOI: 10.1109/81.633878
[31] DOI: 10.1109/81.974874 · Zbl 1368.93576
[32] DOI: 10.1142/9789812778420
[33] DOI: 10.1142/S021812740501220X · Zbl 1079.93019
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.