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The multiagent system has the advantages of simple structure, strong function, and cost saving, which has received wide attention from different fields. Consensus is the most basic problem in multiagent systems. In this paper, firstly, the problem of partial component consensus in the first-order linear discrete-time multiagent systems with the directed network topology is discussed. Via designing an appropriate pinning control protocol, the corresponding error system is analyzed by using the matrix theory and the partial stability theory. Secondly, a sufficient condition is given to realize partial component consensus in multiagent systems. Finally, the numerical simulations are given to illustrate the theoretical results.

In recent years, the theory of consistency, as the basis of coordinated control of multiagent system, has attracted extensive attention from many researchers [

The consistency of the discrete multiagent systems is that the state of all agents in a discrete system model can achieve asymptotic convergence under certain conditions. Many researchers have discussed the consistency problem of multiagent systems [

The consistency of discrete multiagent systems has more advantages than continuous multiagent systems. For example, it can reduce a lot of computation, and the speed of convergence is fast and so on. Therefore, the research of discrete consistency has some practical significance. Wu Binbin et al. have studied the partial component consensus of continuous multiagent systems in [

In detail, the remainder of this paper is organized as follows: Section

In this section, we will give the basic concept of partial component consistency, basic matrix theory, and some definitions and lemmas. For details, refer to [

We consider the following n-dimensional discrete system:

Similar to the definition of partial component stability for continuous system in [

The trivial solution of (

The trivial solution of (

The trivial solution of (

Let

In this section, we consider a first-order discrete multiagent system, which consists of N following agents and a leader, and suppose the equation of state for the following agent is

Supposing the dynamic equation of the leader agent is

Next we consider the problem of partial component conformance of discrete leader-following multiagent system under directed network topology. We design the controller as follows:

Let

In order to discuss the asymptotic stability of the trivial solution of the error system (

If there exist

If there exist

Let

Define the following Lyapunov function candidate:

In this section, a numerical example has been given to show that our theoretical result obtained above is effective.

Given the parameter

Figure

The topology diagram of agent connection.

(a) The state error of the leader-following for the first component. (b) The state error of the leader-following for the second component. (c) The state error of the leader-following for the third component.

In this paper, the partial component consensus has been investigated for the first-order discrete leader-following multiagent system. By establishing the suitable control term and using the matrix theory together with the stability theory, the sufficient conditions for the partial component conformance of the discrete system are derived. Furthermore, a numerical example has been given to illustrate the effectiveness of the present results. As an extension to this work, we plan to discuss the partial component consensus for the high-order discrete leader-following multiagent system.

No data were used to support this study.

The authors declare that they have no conflicts of interest.

The authors gratefully acknowledge the support of the National Natural Science Foundation of China (NNSF) through Grant (No. 11562006), the NSF of Guangxi Province (2018GXNSFAA281068), and the NSF of Shanxi Province (201801D121009).