In Chaps. 3–6, the disagreement behaviors have been explored for fixed signed networks, where their network topologies are represented with fixed signed digraphs and, thus, are restricted to describe the unchanging interactions among agents. However, in many real scenarios, the interactions among agents may change over time due to the impacts from internal or external factors, which renders the behavior analysis approaches and results for fixed signed networks no longer effective. This chapter focuses on signed networks in the presence of switching topologies and is devoted to investigating the uniform convergence behaviors for them. The fundamental properties of steady states of switching signed networks are proposed, where, in particular, the necessary and sufficient conditions on uniform bipartite consensus and uniform asymptotic stability are developed, respectively, without imposing any connectivity conditions. In addition, by adopting a state transition matrix-based analysis approach, we disclose that for any jointly strongly connected signed network, the uniform bipartite consensus (respectively, uniform asymptotic stability) can be achieved if and only if its associated switching signed digraph is simultaneously structurally balanced (respectively, unbalanced). These developed results do not require the assumption on the digon sign-symmetry of signed digraphs and can be guaranteed to have an exponential convergence speed. They benefit from the presented new disagreement behavior analysis approach that bridges a clear relation between signed networks and their induced unsigned networks. Some simulations are performed to illustrate the validity of the uniform convergence results established for switching signed networks.
Uniform Convergence Behaviors
Intelligent Control & Learning Systems
2022-12-03
26 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
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