Delay-Dependent Stability Region for the Distributed Coordination of Delayed Fractional-Order Multi-Agent Systems

Abbasali Koochakzadeh, Mojtaba Naderi Soorki, Aydin Azizi (), Kamran Mohammadsharifi and Mohammadreza Riazat
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Abbasali Koochakzadeh: Department of Electrical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran 1591634311, Iran
Mojtaba Naderi Soorki: Department of Electrical Engineering, Sharif University of Technology, Tehran 1458889694, Iran
Aydin Azizi: School of Engineering, Computing and Mathematics, Oxford Brookes University, Wheatley Campus, Oxford OX33 1HX, UK
Kamran Mohammadsharifi: Department of Electrical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran 1591634311, Iran
Mohammadreza Riazat: Department of Electrical Engineering, K. N. Toosi University of Technology, Tehran 1543319967, Iran

Mathematics, 2023, vol. 11, issue 5, 1-13

Abstract: Delay and especially delay in the transmission of agents’ information, is one of the most important causes of disruption to achieving consensus in a multi-agent system. This paper deals with achieving consensus in delayed fractional-order multi-agent systems (FOMAS). The aim in the present note is to find the exact maximum allowable delay in a FOMAS with non-uniform delay, i.e., the case in which the interactions between agents are subject to non-identical communication time-delays. By proving a stability theorem, the results available for non-delayed networked fractional-order systems are extended for the case in which interaction links have nonequal communication time-delays. In this extension by considering a time-delay coordination algorithm, necessary and sufficient conditions on the time delays and interaction graph are presented to guarantee the coordination. In addition, the delay-dependent stability region is also obtained. Finally, the dependency of the maximum allowable delay on two parameters, the agent fractional-order and the largest eigenvalue of the graph Laplacian matrix, is exactly determined. Numerical simulation results are given to confirm the proposed methodologies.

Keywords: distributed coordination; fractional-order systems; multi-agent systems (MAS); communication time-delay (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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