Chin. Phys. B Vol. 27, No. 1 (2018) 010701 Leader-following consensus of discrete-time fractional-order multi-agent systems Erfan Shahamatkhah and Mohammad Tabatabaei † Department of Electrical Engineering, Khomeinishahr Branch, Islamic Azad University, Isfahan, Iran (Received 2 August 2017; revised manuscript received 31 August 2017; published online 17 November 2017) Leader-following consensus of fractional order multi-agent systems is investigated. The agents are considered as discrete-time fractional order integrators or fractional order double-integrators. Moreover, the interaction between the agents is described with an undirected communication graph with a fixed topology. It is shown that the leader-following consensus problem for the considered agents could be converted to the asymptotic stability analysis of a discrete-time fractional order system. Based on this idea, sufficient conditions to reach the leader-following consensus in terms of the controller parameters are extracted. This leads to an appropriate region in the controller parameters space. Numerical simulations are provided to show the performance of the proposed leader-following consensus approach. Keywords: multi-agent systems, fractional order systems, leader-following consensus, discrete-time fractional order systems PACS: 07.05.Dz DOI: 10.1088/1674-1056/27/1/010701 1. Introduction The application of multi-agent systems in sensor networks, [1] autonomous vehicles, [2] and mobile robots [3] has attracted the researchers to develop new methods for cooper- ative control of multi-agent systems. [4] These methods have been proposed to attain different goals such as consensus, [5] formation control, [6] and flocking. [7] Agreement of all the agents in a multi-agent system is called consensus. In a leader- following consensus, the control signals of the agents are ap- propriately selected such that their state trajectories follow the leader state. [5] This could be achieved by obtaining informa- tion from the leader and other agents. Various works have been reported about leaderless con- sensus and leader-following consensus of multi-agent sys- tems. Hierarchical cooperative control of multi-agent sys- tems with switching directed topologies has been verified in Ref. [8]. In Ref. [9], a novel finite-time stability crite- rion for a linear discrete-time stochastic system with applica- tions to consensus of multi-agent systems has been presented. Distributed node-to-node consensus of multi-agent systems with stochastic sampling has been investigated in Ref. [10]. Distributed observer-based stabilization of nonlinear multi- agent systems with sampled-data control [11] and observer- based consensus tracking of nonlinear agents in hybrid vary- ing directed topology [12] have been studied too. These works include the first order agents (integrator), the second order agents (double-integrator), or high-order agents (with arbitrary number of states). However, in practical applications, con- sensus of multi-agent systems with the first-order or second- order agents is preferred. In Ref. [13], finite-time consensus of second-order multi-agent systems using the auxiliary system approach has been verified. Leader-following consensus of second-order multi-agent systems with fixed and time-varying delays has been studied in Refs. [14] and [15]. In Ref. [16], a leader-following consensus control for first-order multi-agent systems in the presence of measurement noise and commu- nication delays has been proposed. Consensus of second- order discrete-time multi-agent systems with fixed topology has been addressed in Ref. [17]. In Ref. [18], robust finite- time leader-following consensus for second-order multi-agent systems with nonlinear dynamics has been discussed. Finite- time consensus of second-order leader-following multi-agent systems without velocity measurements has been verified in Ref. [19]. In Ref. [20], consensus of second-order multi-agent systems in the presence of velocity constraints has been ver- ified. Moreover, consensus of second-order multi-agent sys- tems with external disturbances has been considered in the literature. [21–23] Fractional order systems have been utilized to describe dynamics of some physical phenomena (like diffusion and vis- coelasticity) with non-integer operators. [24] Dynamical sys- tems could be better described by fractional order systems. For example, the dynamical properties of neural networks could be better described with fractional complex-valued neu- ral networks. [25] Consensus of fractional order multi-agent systems (FOMAS) has been considered in the literature. In Ref. [26], necessary and sufficient conditions for consensus of delayed fractional-order systems have been extracted us- ing the generalized Nyquist stability criterion. The same ap- proach has been employed in Ref. [27] to reach consensus for fractional order systems with simultaneously non-uniform in- put and communication delays. In Ref. [28], sufficient con- † Corresponding author. E-mail: tabatabaei@iaukhsh.ac.ir © 2018 Chinese Physical Society and IOP Publishing Ltd http://iopscience.iop.org/cpb http://cpb.iphy.ac.cn 010701-1