TY  - JOUR
T1  - Observability study in weighted and Directed signed multi-agent networks of Single- and double-integrator dynamical Agents
AU  - Athira, V. S.
AU  - Vijayakumar, S. Muni
AU  - Kallu ,Vetty Muhammed Rafeek
AU  - Aadhithyan, B.
AU  - Gudala,Janardhana Reddy
JO  - Indian Journal of Mathematics
VL  - 67
IS  - 2
SP  - 173
EP  - 205
PY  - 2025
DA  - 2026/07/09
SN  - 0019-5324
KW  - Multi-agent systems
KW  - Observability
KW  - Observability
KW  - Heterogeneous agent models
KW  - Digraphs
KW  - Signed and weighted graphs.
AB  - In this study we examine observability in signed multi-agent networks with a directed, weighted, and time-invariant communication topology. The network follows linear
heterogeneous dynamics, incorporating both first- and second-order integrator agents in continuous time. Agents are classified into sensors (whose state information is fully
known beforehand) and non-sensors (whose state information is completely unknown). The objective is to determine whether it is possible to reconstruct the states of non-sensors using the
knowledge of the sensors, a property referred to as the network’s sensor–non-sensor observability. We formulate the necessary and sufficient mathematical conditions for analyzing this
property by utilizing the rank and spectral characteristics of the matrices governing the dynamics. These conditions are applied to various networks to assess their observability, demonstrating
the effectiveness of the results presented. Our findings indicate that the sensor–non-sensor observability property in signed, directed, and weighted networks generally differs from that of
their unsigned, undirected, and unweighted counterparts.
ER  -