Distributed complex consensus in hybrid networks: A complex Laplacian‐based approach
Mana Donganont · Asian Journal of Control · 2025
Abstract This paper addresses complex consensus in hybrid multi‐agent systems (HMASs) comprising continuous‐time (CT) and discrete‐time (DT) agents over complex‐weighted networks. Existing work has largely treated real‐valued hybrid consensus or complex consensus in homogeneous systems, leaving phase‐coherent coordination across hybrid time domains underexplored. We propose a sampled‐data framework based on complex Laplacians that unifies CT and DT dynamics and introduce two distributed protocols, one with static feedback and the other with real‐time self‐observation for CT agents. A diagonal unitary transformation reduces the complex dynamics to a real‐valued form, enabling spectral analysis. Necessary and sufficient conditions for convergence in modulus and phase are established, with simulations on both small‐ and large‐scale networks validating the theory. The approach offers a scalable method for geometric coordination in hybrid systems.