Stability of dynamical networks with non-identical nodes: A multiple V-Lyapunov function method

Jun Zhao*, David J. Hill, Tao Liu

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    66 Citations (Scopus)

    Abstract

    Global asymptotic stability of general dynamical networks with non-identical nodes is studied by introducing multiple V-Lyapunov functions. In such a network, the coupling strength, inner coupling matrix and outer coupling matrix are all allowed to be state-dependent and nonlinear. A stability criterion is proposed in terms of matrix norms and eigenvalues of some lower-dimensional matrices. Based on this criterion, an optimization problem is formed whose solution can be used to test global asymptotic stability. We also study the problem of how to achieve global asymptotic stability by design of controllers under the scheme of multiple V-Lyapunov functions. The control action is regarded as a re-shape of outer coupling topology and the associated controllers are designed. In particular, a method of adding or removing a certain number of links is proposed. Stability analysis of coupled non-identical Lorenz systems and a design example are also given to illustrate the proposed method.

    Original languageEnglish
    Pages (from-to)2615-2625
    Number of pages11
    JournalAutomatica
    Volume47
    Issue number12
    DOIs
    Publication statusPublished - Dec 2011

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