Observability Study in Weighted and Directed Signed Multi-Agent Networks of Single- and Double-Integrator Dynamical Agents

V. S., Athira; Muni, Vijayakumar S.; Vetty, Muhammed Rafeek Kallu; B., Aadhithyan; Reddy, Gudala Janardhana

Indian Journal of Mathematics

Observability Study in Weighted and Directed Signed Multi-Agent Networks of Single- and Double-Integrator Dynamical Agents

Author(s): Athira V. S. Athira V. S. Department of Mathematics,
Central University of Karnataka,
Kadaganchi P. O., Kalaburagi District 585367, Karnataka,
India. athiravikraman884@gmail.com , Vijayakumar S. Muni Vijayakumar S. Muni Department of Mathematics,
Smt. Indira Gandhi Govt. First Grade Women’s College,
Sagara P. O., Shivamogga District, 577401, Karnataka,
India. vijayakumarmuni0@gmail.com , Muhammed Rafeek Kallu Vetty Muhammed Rafeek Kallu Vetty Department of Mathematics,
National Institute of Technology Andhra Pradesh,
Tadepalligudem P. O., West Godavari District, 534101,
Andhra Pradesh,
India. rafeekkv997@gmail.com , Aadhithyan B. Aadhithyan B. Department of Mathematics,
Central University of Karnataka,
Kadaganchi P. O., Kalaburagi District 585367, Karnataka,
India. aadhithyan96@gmail.com , Gudala Janardhana Reddy Gudala Janardhana Reddy Department of Mathematics,
Central University of Karnataka,
Kadaganchi P. O., Kalaburagi District 585367, Karnataka,
India. gjr@cuk.ac.in

Vol. 67, No. 2 (2025) • pp. 173–205

Published 09-07-2026 Article History Received 13-06-2025 Revised 04-03-2026 Published 09-07-2026

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Abstract

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.

Keywords

Multi-agent systems, Observability, Heterogeneous agent models, Digraphs, Signed and weighted graphs.

2020 Mathematics Subject Classification

93A16, 93B07, 91B69, 05C20, 05C22.

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Allahabad Mathematical Society

Observability Study in Weighted and Directed Signed Multi-Agent Networks of Single- and Double-Integrator Dynamical Agents

Abstract

Keywords

2020 Mathematics Subject Classification

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