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Stability of continuous-time distributed consensus algorithms

Stability of continuous-time distributed consensus algorithms,10.1109/CDC.2004.1429377,Luc Moreau

Stability of continuous-time distributed consensus algorithms   (Citations: 130)
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We study the stability properties of linear time-varying systems in continuous time whose system matrix is Metzler with zero row sums. This class of systems arises naturally in the context of distributed decision problems, coordination and rendezvous tasks and synchronization problems. The equilibrium set contains all states with identical state components. We present sufficient conditions guaranteeing uniform exponential stability of this equilibrium set, implying that all state components converge to a common value as time grows unbounded. Furthermore it is shown that this convergence result is robust with respect to an arbitrary delay, provided that the delay affects only the off-diagonal terms in the differential equation.
Conference: Conference on Decision and Control - CDC , vol. 4, pp. 3998-4003 Vol.4, 2004
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    • ...In Moreau and Belgium (2004), a sufficient condition was derived to ensure the networks with the time-dependent communication patterns and a common time delay in communication between distinct agents to reach consensus asymptotically...

    Yurong Liuet al. A new framework for consensus for discrete-time directed networks of m...

    • ...The authors in [12] showed that communication delays will not jeopardize the stability of the first-order leaderless consensus algorithm under a directed network topology...
    • ...Third, we show that the communication delay will not influence the stability of the firstorder system in the case of consensus tracking with partial access to the virtual leader, which extends the results of [12] and [17]...

    Ziyang Menget al. Leaderless and Leader-Following Consensus With Communication and Input...

    • ...A1 = 0. This types of systems have been well characterized by Moreau [40]...

    Federica Garinet al. A Survey on Distributed Estimation and Control Applications Using Line...

    • ...The Partial difference Equation (PdE) framework is used in [29] to show that Laplacian control, analyzed in [30] and [31], coincides with the heat equation...

    Paul Frihaufet al. Leader-Enabled Deployment Onto Planar Curves: A PDE-Based Approach

    • ...<{[SECTION]}>[14] Z. Sun and S. Ge, “Analysis and synthesis of switched linear control...
    • ...Thus, in [14] and [38] the integral connectivity is proposed to study consensus problem...
    • ...In [9], [10], [14], [33], is assumed piecewise continuous, in addition the entries of the weighted adjacency matrix are with a uniformly lower bound above zero, i.e., . One also finds in some literature that some constraints were applied on the time axis...
    • ...In [10], [14], [29] the time axis is partitioned into time intervals such that is continuous on each interval...
    • ...In [10], [29] it is assumed that the interval lengths are with uniformly lower bound above zero, i.e., , for all . In [14] the interval lengths are equal to a constant...

    Li Caoet al. A Necessary and Sufficient Condition for Consensus of Continuous-Time ...

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