Response Letter
Paper number: NODY-D-15-00088
Paper title: Event-Triggered Control for Multi-Agent Network with Limited Digital Communication
Authors:
Dear Editor-in-chief, Associate Editor and Anonymous Reviewers,
We would like to thank you for your efforts in reviewing our manuscript and providing many helpful comments and suggestions. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments very carefully. Based on your criticisms, comments and suggestions, we have revised the manuscript accordingly. The details are explained below, where the number of the response is in correspondence with the number of the reviewers’ comments and su ggestions.
Reply to the Associate Editor
According to the AE’s and reviewers’ criticisms, comments and suggestions, we have modified the manu
script carefully. The description of a substantial revision and the detailed points to the review reports can be seen in the following responses and in the new revision. Moreover, we have also checked other derivations throughout the paper and some necessary explanations are also included.
We would like to thank the reviewer’s great efforts in reading our manuscript and for your constructive comments and suggestions. Our responses to the comments and suggestions are listed as follows:
1. Consensus with communication constraints is indeed a quite interesting topic in field of multi-agent systems, the following work on consensus of second-order multi-agent systems may be briefly mentioned: Int. J. Robust and Nonlinear Control, 22(2):170-182, 201
2.
editor suggestionReply:The relevant works of communication constraints in Int. J. Robust and Nonlinear Control is really worth mentioning, and this reference has been added in new revision.
2. The communication topology is assumed to be undirected, whether it is possible to do some further work on directed or switching topologies. One more remark may be added to the manuscript to state this issue.
Reply:This suggestion is very nice and reasonable. The directed and switching topologies cases will be our future works, and the remark has been provided in the future works part of conclusion.
We would like to thank the reviewer ’s  great efforts in reading our manuscript and for your constructive comments and suggestions. Our responses to the comments and suggestions are listed as follows:
1. The proof of Theorem 1 is not clear. It didn’t show what is the convergence set
very important obviously.
Reply: This suggestion is very helpful, and I have rewritten the Theorem 1. I’m sure the new version is much clearer than the old one.
2. There are some errors in the proof of Theorem 1. For example,
(i) How to determine l in the last line of formula (16). There is no any constraint for l.
(ii) The same problem appeared in the last line and previous line of formula (18).
Reply: I am very sorry for my carelessness. The last expression ˆ(t )l l
l k x
in formula (16) and (18) should be replaced by ˆ(t )i i
i k x
. Now the total four mistakes in formula (16) and (18) have been corrected in revised version. To avoid the similar mistakes, I have also checked the other derivations throughout the manuscript. Again thanks for your carefulness and tolerance.
3. What is the function of parameter i σ in the event triggering condition (8). Which performance does it affect? How to choose this parameter according to the demands of performance? The analysis should be given.
Reply: This suggestion is very reasonable. Actually, this parameter’s main function is to adjust the performance of event triggering mechanism. Each agent’s event frequency has a great relationship with the parameter i σ. The larger i σ, the event
times are less and the performance is better. To obtain the best performance, we directly set 1
σ=in revised version, i.e., we no longer define this parameter i
explicitly in revised version.

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