Global synchronised regions of linearly coupled Lur'e systems

• Published in: International journal of control Vol. 84; no. 2; pp. 216 - 227
• Main Authors: Li, Zhongkui, Duan, Zhisheng, Chen, Guanrong
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01.02.2011; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Applied sciences; complex network; Computer science; control theory; systems; control; Control system analysis; Control theory. Systems; Exact sciences and technology; global synchronisation; Lur'e system; Nonlinear dynamics and nonlinear dynamical systems; Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems; Studies; synchronised region; Disturbance rejection; Necessary and sufficient condition; global synchronisation; Complex system; H infinite control; H; complex network; Matrix inequality; control; Dynamical system; Synchronization; Non linear system; Electric circuit; System with n degrees of freedom; Decoupling; Lur'e system; Network; synchronised region; Lur'e control
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207179.2010.546882

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 ∞ 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.