Observability Analysis on Discrete-Time Matrix-Weighted Multi-Agent Systems

Unmanned systems are advancing rapidly, driving widespread attention to multi-agent systems composed of clustered consumer electronic devices. Accurately and timely estimating component states of multi-agent systems during signal transmission is critical for performance. However, existing studies primarily focus on observability in scalar-weighted networks, neglecting matrix-weighted alternatives. These matrix-weighted networks provide greater structural complexity and enhanced modeling capabilities for real-world discrete-time communication models. This paper addresses the observability gap in discrete-time multi-agent systems over matrix-weighted networks, a domain neglected in existing scalar-weighted studies. The observability conditions for systems with fixed weights are first established. The observability criteria are established via spectral decomposition and graph theory, analyzing two eigenvalue distribution cases of the system state matrix. Subsequently, observability criteria for systems with time-varying weights are derived. The criteria are derived using algebraic graph theory, yielding graphical and algebraic conditions based on specific topological configurations. Computational studies validate the effectiveness of the proposed conditions.