Akademik Veri Yönetim Sistemi
Neurocomputing, cilt.672, 2026 (SCI-Expanded, Scopus)
This paper investigates the matrix-weighted cluster consensus problem in general directed networks which finds applications in synchronization of oscillators, formation control and coordinated movement of multi robot systems. Unlike previous studies that assume restrictive topological conditions such as spanning trees or strong connectivity, and primarily focus on scalar-weighted or undirected networks, this work develops a theoretical framework for matrix-weighted cluster consensus in systems represented by general directed graphs where edge weights are represented by positive definite or negative definite matrices. This generalization enables the analysis of consensus dynamics in systems characterized by vector-valued states and complex interaction structures. We provide conditions to determine the number and structure of clusters that emerge in such networks by using the concepts of primary and secondary layer subgraphs. Additionally, the analysis is extended to discrete-time systems, where a distributed approach for step-size selection ensures stability and convergence to multiple clusters. This distributed approach only requires agents to have partial local information, making it scalable to large networks. Numerical simulations validate our theoretical findings in multi-agent systems with matrix-weighted dynamics.