-->-->PONE-D-26-08045-->-->Observer-based prescribed-time lag bipartite consensus of nonlinear multi-agent systems under event-triggered mechanism-->-->PLOS One

Dear Dr. Li,

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PLOS One

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Thank you for stating the following financial disclosure: -->-->Tao Li received the funding of the National Natural Science Foundation of China under Grant number 62473135, Xiaowen Zhao received the funding of the National Natural Science Foundation of China under Grant number 62173121, Le Yan received the Natural Science Foundation of Hubei Province of China under Grant number 2024AFB812.  -->--> -->-->Please state what role the funders took in the study.  If the funders had no role, please state: "The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript." -->-->If this statement is not correct you must amend it as needed. -->-->Please include this amended Role of Funder statement in your cover letter; we will change the online submission form on your behalf.-->--> -->-->4. 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Additional Editor Comments:

In light of the reviewers’ comments, the manuscript is considered to have potential for publication, provided that appropriate and necessary revisions are made. The authors are kindly requested to carefully address these comments and further improve the manuscript accordingly.

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Reviewers' comments:

Reviewer's Responses to Questions-->

-->Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.-->

Reviewer #1: Yes

Reviewer #2: Yes

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-->2. Has the statistical analysis been performed appropriately and rigorously?-->

Reviewer #1: Yes

Reviewer #2: Yes

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-->3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #1: No

Reviewer #2: No

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-->4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.-->

Reviewer #1: Yes

Reviewer #2: Yes

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-->5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)-->

Reviewer #1: This manuscript studies the observer-based prescribed-time lag bipartite consensus problem for nonlinear multi-agent systems under an event-triggered mechanism. The topic is relevant, and the integration of prescribed-time observer design, event-triggered communication, and lag bipartite consensus is potentially interesting. However, the following comments must be considered:

1. The notation system and several basic definitions need substantial revision.

2. Theorem 2 invokes Assumptions 1, 2, and 3, but Assumption 3 is not explicitly stated in the provided preliminaries.

3. The prescribed-time design and the time parameters T, T_1, T_2, and T_3 should be clarified much more carefully.

4. The main proofs, especially for Theorems 1 and 2, rely on several matrix inequalities and positive-definiteness claims, but the derivations are presented too briefly. In particular, the manuscript needs to justify more explicitly why the chosen Lyapunov functions are positive definite under the proposed parameter conditions, and how the bounds are transformed step by step.

5. The Introduction would benefit from citing and discussing several references relevant to the research methodology, which could further enrich the background on nonlinear control and event-triggered control, such as 10.1016/j.automatica.2024.111511, 10.1016/j.automatica.2022.110792, and 10.1109/TIE.2026.3654623.

Reviewer #2: This paper aims to address the prescribed-time lag bipartite consensus control problem for nonlinear multi-agent systems. Generally, this is a well written and organized article with interesting theoretical results proposed. However, some concerns have to be addressed for better qualification:

The contribution should be stated by comparing with the existing results, therefore, the novelty should be further improved and highlighted.

The reasonability and references of assumptions should be given.

Some latest results about finite-time control should be introduced such as tuning function-based light computational adaptive fixed-time control for overhead cranes with multiple uncertainties, security-driven adaptive iterative learning formation control for multiagent systems etc., to make the review complete.

Fig. 4 is unclear, please revise it.

Some comparison results should be shown to explain the novelty of the proposed method.

The future work should be added to the conclusion.

The linguistic quality or grammar problems need improvement, such as "\beta are the observer gains" etc. The authors should pay attention to these problems.

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Reviewer #1: No

Reviewer #2: No

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Observer-based prescribed-time lag bipartite consensus of nonlinear multi-agent systems under event-triggered mechanism

PONE-D-26-08045R1

Dear Dr. Li,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Hongru Ren

Academic Editor

PLOS One

Additional Editor Comments (optional):

The revised manuscript has been re-reviewed by multiple reviewers and has received favorable evaluations and unanimous approval from all of them. After carefully assessing the reviewers’ comments and the overall academic quality of the manuscript, I fully agree with the reviewers’ judgments and recommendations.

Reviewers' comments:

Reviewer's Responses to Questions

-->Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.-->

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

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-->2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. -->

Reviewer #1: Yes

Reviewer #2: Yes

**********

-->3. Has the statistical analysis been performed appropriately and rigorously? -->

Reviewer #1: Yes

Reviewer #2: Yes

**********

-->4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #1: Yes

Reviewer #2: Yes

**********

-->5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.-->

Reviewer #1: Yes

Reviewer #2: Yes

**********

-->6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)-->

Reviewer #1: The authors have addressed all my concerns. I think this paper can be accept now. Good luck to the authors.

Reviewer #2: This paper has been revised well. I have no further comments. As a result, I suggest that it can be accepted.

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-->7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.-->

Reviewer #1: No

Reviewer #2: No

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