An Output Feedback Controller for a Second-Order System Subject to Asymmetric Output Constraint Based on Lyapunov Function with Unlimited Domain

Round 1

Reviewer 1 Report

The reviewer has the following comments and suggestions:

1. The authors should provide some simulation comparisons with other related control strategies to verify the effectiveness and advantages of the proposed approach; 2. Assumption 1 is not very clear: "The state ?2 is bounded for ? bounded", is it "The state ?2 is bounded if ? is bounded"?; 3. Assumption 2 is not very clear: "The state ?1 is known and ? is known". is it "The state ?1 is measurable and ? is known"?

Author Response

Reply Reviewer # 1

Thanks to the reviewer #1 for his feedback.

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Reviewer 2 Report

This paper propose a robust controller for second order plant model with asymmetric output constraint. There exist some interesting results, and the following suggestions should be considered.

1. In the system dynamic (1), the definition of $F_g1$ should be given.

2. In the observer (3), you define the $Had1, H_g1, H_ad2, b_m $ are the known functions. However, I think the internal model of the observer should be designed based on the information of the dynamics.

3. Input constraints was considered in your results. Howerver, the bound of $U_max$ and $U_min$ are constant. How do you chose both constants?

4. The disadvantage of the proposed method should be described in conclusion.

Author Response

Reply Reviewer # 2

Thanks to the reviewer # 2 for his feedback.

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Reviewer 3 Report

In this work, a new robust controller is designed for second order plant model,
considering asymmetric output constraint. This topic is interesting and has some
novelties. The analysis seem correct and the established conclusions are right. This
paper can be accepted after the following points have been taken into account:
1. Compared with the previous publications, what is the advantage of the
robust controller of this paper?
2.The motivation of this paper shall be improved.
3. What are the advantages and disadvantages of this robust controller?
4. Which technique is used in numerical simulations?
5. Some related publications on control of dynamical systems shall be added
to emphasize the latest research progress. e.g.,
1) Fixed-time synchronization for complex-valued BAM neural networks with
time-varying delays via pinning control and adaptive pinning control. Chaos Solitons
Fractals 2021, 153, 111583
2) Theoretical analysis and computer simulations of a fractional order bank data
model incorporating two unequal time delays, Expert Systems with Applications 199
(2022) 116859
3) Dynamic Analysis and Bifurcation Study on Fractional-Order Tri-Neuron Neural
Networks Incorporating Delays, FRACTAL AND FRACTIONAL,6(3),2022,Article
Number: 161, https://doi.org/10.3390/fractalfract6030161

Author Response

Reply Reviewer # 3

Thanks to the reviewer # 3 for his feedback.

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Author Response File: Author Response.pdf

Reviewer 4 Report

This article addresses an interesting and challenging topic in output feedback control of 2nd order systems.

The intro and literature review give enough insight to the reader about the significance of the work and the merit of the proposal.

The detailed derivations and theorem presentation are well-written and easy to follow. 

However, I would like to have more clarification for the scope and impact of the assumptions 1,2,3. What is the implication of these assumptions in a practical way and constrains that these can potentially impose on the approach.

The results are clear and supporting the proposal.

I would like to see more discussion regards to potential applications of the work.

 

Author Response

Reply Reviewer # 4

Thanks to the reviewer # 4 for his feedback.

I attach the document with the answers

Author Response File: Author Response.pdf

Reviewer 5 Report

Taking the second-order system as the research object, the author designs a new robust controller based on Lyapunov theory. The writing level of the thesis is high. The theory has certain innovations. It is of great reference value for dynamic models. But reviewers felt that the paradigm in the simulation was too simplistic. In conclusion, the reviewers considered the paper to be acceptable.

Author Response

Reply Reviewer # 5

Thanks to the reviewer # 5 for his feedback.

I attach the document with the answers

Author Response File: Author Response.pdf