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

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.

Automated summary

This paper addresses the issue of achieving consensus in delayed fractional-order multi-agent systems (FOMAS). By extending the results of non-delayed networked fractional-order systems, the stability of FOMAS with non-identical communication time-delays is analyzed. Necessary and sufficient conditions for coordination are presented by considering a time-delay coordination algorithm. The relationship between the maximum allowable delay and the agent fractional-order and the largest eigenvalue of the graph Laplacian matrix is determined, and numerical simulations confirm the proposed methodologies.