In Chap. 7, the uniform convergence behaviors have been exploited for signed networks subject to jointly strongly connected switching topologies. In particular, the uniform bipartite consensus and uniform asymptotic stability have been, respectively, tied to the simultaneous structural balance and unbalance of jointly strongly connected signed networks, which is similar to the convergence analysis results for fixed signed networks in Chap. 3. A question arises: Whether may similar convergent behaviors still emerge for switching signed networks as those for fixed signed networks without the joint strong connectivity condition? In the current chapter, we provide a negative answer to this question by focusing on jointly quasi-strongly connected signed networks. A class of fluctuation behaviors, i.e., the quasi-interval bipartite consensus, is newly discovered for switching signed networks. To be specific, only the joint root agents are ensured to converge and realize uniform bipartite consensus, whereas the joint non-root agents may not converge but fluctuate within the converged states of joint root agents and their symmetric states. By resorting to the state transition matrix-based analysis approach, it is shown that the quasi-interval bipartite consensus (respectively, uniform asymptotic stability) can be achieved for any jointly quasi-strongly connected signed network if and only if its related signed digraph admits a s.s.b. (respectively, s.s.ub.) joint-rooted subgraph. Illustrative examples are provided to validate the fluctuation results of switching signed networks under the joint quasi-strong connectivity condition.
Quasi-Interval Bipartite Consensus
Intelligent Control & Learning Systems
2022-12-03
20 pages
Article/Chapter (Book)
Electronic Resource
English
Springer Verlag | 2022
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