Distributed Control Problems on Signed Networks under Mixed Static and Dynamic Protocols

This article aims at exploring the dynamic behaviors of signed networks under the mixed static and dynamic control protocols, which reflect the existence of two classes of communication channels. An extended leader-follower framework admitting multiple dynamic leaders is established to identify the roles of all nodes in signed networks, depending on the union of two related signed digraphs. It is shown that bipartite containment tracking is achieved for signed networks despite any topology conditions. To be specific, every leader group realizes modulus consensus and the leaders dominate the dynamic evolutions of signed networks such that all followers converge within the bounded zone spanned by the leaders' converged states and their symmetric states. Furthermore, conditions on the zero convergence of dynamic control inputs are exploited, together with those on the (interval) bipartite consensus of signed networks. Simulation examples are given to demonstrate the convergence behaviors of signed networks with respect to the mixed static and dynamic control protocols.