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The leader-following consensus problem for delayed multiagent systems is investigated over stochastic switching topologies via impulsive control method. A distributed consensus protocol is proposed based on sample data information. The convergence analysis for such algorithm over undirected and directed networks is provided, and some sufficient conditions to guarantee the consensus are also established. It is shown that delayed networks can achieve consensus even information is exchanged among followers just at some discrete moments. At last, some numerical examples are given to illustrate the effectiveness of the proposed protocols.

Recently, there has been an increasing attention in the consensus problems of multiagent systems because of their wide applications in many fields such as flocking [

As we know, in the real world, especially in neural processing and signal transmission, time delay has to be taken into consideration [

It should be noticed that in practical life, some biological and physical systems are characterized by abrupt changes of states at some time instants [

To the best of our knowledge, the leader-following consensus problem is becoming more and more popular recently [

Motivated by the aforementioned works, we study leader-following consensus of delayed multiagent systems via impulsive control and propose a protocol based on sampled data information. Compared with pure discrete-time or pure continuous-time model, this problem is more complicated. The analysis becomes difficult if the time delay is time-varying and the topology is switching. We analyse this problem by virtue of algebraic graph theory, the Lyapunov control approach, and generalized Halanay inequality. The contribution of this paper is threefold. First, we propose a more practical protocol by considering communication delay, impulsive effect, and leader-following configuration. Second, without assuming that the interaction graph is strongly connected (connected) or balanced, or has a directed spanning tree, we study this problem over general network topologies. Third, we generalize the works of [

The paper is organized as follows. Section

Throughout this paper, some mathematical notations and definitions are used here. Let

Let the function

We use a graph to describe the information exchange among agents in a multiagent system. Let

A path from node

Many people studied the first-order consensus protocol as follows [

For example, Olfati-Saber and Murray studied this protocol over undirected networks with constant time delay and fixed topology and suggested that the network topology and the designed protocol are very important to the performance and the communication cost [

The dynamics of the leader are described as follows:

Without loss of generality, we suppose that

Let

Recently, many works studied consensus problem, and most of the network topologies are assumed to be connected (strong connected) or have a spanning tree [

In this section, we will give convergence analysis of this problem over undirected and directed networks, respectively. From the system (

Suppose that every communication topology in

Since the Laplacian matrix

Construct a Lyapunov function

Since

So for

For

Combine with (

Suppose that node 0 is globally reachable in every communication topology of

Suppose that in the time interval

Define the Lyapunov function as

Since

If

The result of Theorem

In this paper, only sufficient condition is derived; that is, the system (

In [

Wu et al. [

In this section, we provide simulations to illustrate the effectiveness and advantages of the proposed algorithms. Obviously, from Figure

Topologies (a)–(d) are studied by our model, whereas topologies (e)–(h) are studied by [

In this simulation, the interaction topology switches randomly every 0.1 s among

The trajectories of agents in the system (

In this simulation, the interaction topology switches randomly every 0.1 s among

(a)-(b) are figures of system (

In this section, we address advantages of our model via simulation as discussed in Remarks

In this paper, we study leader-following consensus problem of delayed multiagent systems with impulsive effects over a general network topology and propose a protocol based on sample data information. Some sufficient conditions are obtained to guarantee that the followers converge to the leader globally exponentially. We show that under this impulsive protocol, the delayed networks can achieve consensus even the followers exchange information with each other only at some discrete moments. Some simulations are given to verify the effectiveness of the theoretical results. The time-saving and energy-saving of the protocol are also shown via simulations.

The authors declare that there is no conflict of interests regarding the publication of this paper. This paper is new. Neither the entire paper nor any part of its content has been published or has been accepted elsewhere. It is not being submitted to any other journal. All authors have seen the manuscript and approved to submit to your journal.

The authors are grateful to the Associate Editor and the anonymous reviewers for their valuable comments and suggestions that helped improve the presentation of the paper. This work was partially supported by the National Science Foundation of China (Grant no. 61364003) and the Science and Technology Foundation of Guizhou Province (no. 20122316).