Synchronization in networks of identical linear systems

• Published in: Automatica (Oxford) Vol. 45; no. 11; pp. 2557 - 2562
• Main Authors: Scardovi, Luca, Sepulchre, Rodolphe
• Format: Journal Article Web Resource
• Language: English
• Published: Kidlington Elsevier Ltd 01.11.2009; Elsevier; Pergamon Press - An Imprint of Elsevier Science
• Subjects: Applied sciences; Artificial intelligence; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Consensus; Dynamical systems; Dynamics; Engineering, computing & technology; Exact sciences and technology; Ingénierie, informatique & technologie; Joining; Linear systems; Multi-agent systems; Networks; Oscillator analysis; Output feedback; Software; Synchronism; Synchronization; Weak coupling; Weak coupling; Synchronization; Consensus; Multi-agent systems; Oscillator analysis; Connected graph; State space method; Distributed system; Linear model; Time varying system; Multiagent system; Communication graph; Artificial intelligence; Linear space
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2009.07.006

The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected. The result can be interpreted as a generalization of classical consensus algorithms. Stronger conditions are shown to be sufficient–but to some extent, also necessary–to ensure synchronization with the diffusive static output coupling often considered in the literature.