Conditions for Synchronizability in Arrays of Coupled Linear Systems

By S. E. Tuna. 2008

256 citations recorded by the source corpus.

Synchronization in arrays of coupled continuous-time linear systems is studied. Sufficiency of certain conditions for the existence of a synchronizing feedback law are analyzed. It is shown that, for neutrally stable systems that are detectable from their outputs, a linear feedback law exists under which any number of coupled systems synchronize provided that the (directed, weighted) graph describing the interconnection is fixed and connected. An algorithm generating one such feedback law as well as the trajectory that the solutions converge to are presented. It is also shown that, for critically unstable systems, detectability is not sufficient, whereas full-state coupling is, for the existence of a linear feedback law that is synchronizing for all coupling configurations described by a connected graph.

Subfields: Computer Networks and Communications

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In Computer Networks and Communications

1. Wei Ren
2. Zhongkui Li
3. Z. Duan
4. Frank L. Lewis
5. Guanghui Wen
6. Yongcan Cao
7. Guanrong Chen
8. Xiangdong Liu

Citations in the corpus

• Decentralized event-triggered consensus with general linear dynamics (2014, background): “Similar work was presented in Tuna (2009).”
• Designing Fully Distributed Consensus Protocols for Linear Multi-Agent Systems With Directed Graphs (2013, background): “As pointed in [8], for the case where the agents are not neutrally stable, e.”
• Event-triggered communication and control of networked systems for multi-agent consensus (2017, background): “…systems with linear dynamics and assuming continuous communication has been extensively studied, e.g., Li, Duan, and Chen (2011), Li, Duan, Chen, and Huang (2010), Ma and Zhang (2010), Ren (2008b), Scardovi and Sepulchre (2009), Seo, Shim, and Back (2009), Su and Huang (2012) and Tuna (2008, 2009).”
• Decentralized finite-time sliding mode estimators and their applications in decentralized finite-time formation tracking (2010, background): “Consensus for systems with general linear dynamics was studied in [25,26].”
• Distributed robust consensus control of multi-agent systems with heterogeneous matching uncertainties (2013, background): “The agents (2) can recover the nominal linear agents in [9,10,29,20,19,11,22,23] when the uncertainties fi(xi, t) do not exist.”
• Distributed consensus of linear multi-agent systems with adaptive dynamic protocols (2011, unknown): “However, in [16] the protocol is based on the relative states of neighboring agents and the agent dynamics are restricted to be neutrally stable.”
• Dynamic Consensus Networks with Application to the Analysis of Building Thermal Processes (2011, background): “Most of our notation and results follow Tuna (2009); Egerstedt and Ji (2007); Caughman and Veerman (2006); and Ren et al. (2003).”
• Constructing consensus controllers for networks with identical general linear agents (2010, background): “Recently, Li ([11]) and Tuna ([9, 10]) gave conditions for consensus, for networks with agents having identical but general linear internal dynamics and with topology described by directed Laplacian matrices.”
• Consensus of Multi-Agent Systems With General Linear and Lipschitz Nonlinear Dynamics Using Distributed Adaptive Protocols (2011, background): “However, contrary to this technical brief, output feedback controllers have been employed in [14], [16], [17].”