Abstract
This paper is devoted to the convergence problem for second-order signed networks that are associated with two signed graphs in the presence of heterogeneous topologies. An eigenvalue analysis approach is presented to develop convergence results for second-order signed networks, which employs a sign-consistency property for signed graph pairs. When the sign-consistency of two heterogeneous signed graphs and the connectivity of their union are given, bipartite consensus (respectively, state stability) can be derived for second-order signed networks if and only if the union signed graph is structurally balanced (respectively, unbalanced). Two examples are provided to illustrate the effectiveness of the obtained results.
Highlights
Networks involving multiple nodes have received considerable attention from various application fields recently, such as unmanned aerial vehicles, formation satellites and mobile robots
We introduce a class of sign-consistency properties for pairs of signed graphs, based on which an eigenvalue analysis approach to exploring the convergence results of the second-order signed networks is developed
MAIN RESULTS we aim at exploring convergence analysis for secondorder signed networks given by (1) and (2)
Summary
Networks involving multiple nodes (vertices or agents) have received considerable attention from various application fields recently, such as unmanned aerial vehicles, formation satellites and mobile robots. Though in [29], an attempt has been made to accommodate bipartite consensus problems for signed networks with heterogeneous topologies, it is achieved only by extending the network-to-network control results of [30] It is even unclear what the eigenvalues are distributed for second-order. When the two signed graphs representing heterogeneous topologies are sign-consistent and their union is connected, second-order signed networks can achieve bipartite consensus (respectively, state stability) if and only if the union of the two signed graphs is structurally balanced (respectively, unbalanced).
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