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

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.

Hybrid finite‐time fault‐tolerant consensus control of non‐linear fractional order multi‐agent systems based on fault detection and estimation

“…Until 2010, most articles on the stability in MAS only dealt with systems having integer order dynamics. While the control of multi-agent or swarm systems with fractional-order dynamics has attracted the attention of many researchers in recent decades [18][19][20][21], the authors in [20] consider the cooperative control of consensus in fractional-order MAS with the agent model assumed to be a double-integrator. Furthermore, the determination of the maximum allowable communication delay to achieve consensus in a delayed fractional-order MAS is also explored in [21].…”

“…While the control of multi-agent or swarm systems with fractional-order dynamics has attracted the attention of many researchers in recent decades [18][19][20][21], the authors in [20] consider the cooperative control of consensus in fractional-order MAS with the agent model assumed to be a double-integrator. Furthermore, the determination of the maximum allowable communication delay to achieve consensus in a delayed fractional-order MAS is also explored in [21]. The iterative learning consensus control method for MAS, where the agent model is a distributed parametric fractional order, has been implemented in [22].…”

“…Consider the fractional order multi-agent system (5) which is rewritten as (13) along with Assumption 3.1. Now, by applying the observer in (17) to (21), where the coefficients k i , i = 1, 2, 3 are obtained using the following relation:…”