Linear cluster consensus algorithms for signed delayed networks

İngilizce (OpenAlex)

In this study, we investigate the cluster consensus problem for higher-order integrator networks modelled via signed digraphs with delayed dynamics. Contrary to the related studies in the existing literature, systems do not have to contain any special graph structures. By utilising an extended digraph approach, the trajectories of a signed delayed network are recovered from its corresponding extended unsigned digraph. For higher-order integrator systems with fixed input or communication delay under continuous-time topology, the stability properties are investigated and the upper bounds are determined so that the systems achieve cluster consensus without any change in cluster members. Furthermore, we show that the discrete-time higher-order integrator systems with nonuniform delay reach cluster consensus and are stable under bounded delay provided that the undelayed system is stable. At the end, numerical examples are provided to illustrate theoretical results.