Positivity-Preserving H∞ Model Reduction for Discrete-Time Positive Systems via a Successive Convex Optimization Algorithm
Round 1
Reviewer 1 Report
The article give an $H_{\infty}$ model-reduction method while preserving positivity. A sufficient condition for the existence of the desired reduced-order system has been demonstrated in the form of LMI. The results were checked by an example in Section 4. The introduction contain relevant references. The method described here are clear presented.
The authors clearly stated the main contributions of this paper, i.e. propose a positivity-preserving model-reduction scheme, and develop an SCO algorithm for resolving a type of BMI problem without parametrization techniques. Moreover, for achieving a smaller approximation error the zero initial condition is adapted to iterate the reduced-order model which simplifies the design process by abolishing the initialization step.
I recommend this paper for publication in this journal.
Author Response
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Reviewer 2 Report
Comments for author File: Comments.pdf
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Reviewer 3 Report
1. Survey of existing literature is not sufficient. It would useful to include in the Introduction of the paper some discussion on other possible real applications of the obtained results.
2. Some notations in equations have not been defined, see eq. 2, eq. 12.
3. There is no quantitative evaluation in the simulated results. The authors have to give numerical Tables which report the quantitative comparison. The numerical comparison has to be conducted in terms of transient dynamics.
4. The deep discussion is required in simulated results.
5. The conclusion is descriptive. It is void of quantitative and numerical improvement and comparison and the conclusion has to be extended with future work.
6. The author needs to give some practical examples to support the work.
Author Response
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Reviewer 4 Report
The authors discussed on the inner-approximation strategy, 20 we approximate the bilinear constraints with convex ones, under which an iterative procedure is 21 provided to calculate the desired reduced-order model. This work is good and interesting. So I have accepted this paper for publication.
Author Response
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Reviewer 5 Report
This paper considers the positivity-preserving model reduction for discrete-time positive systems.
Generally, the topic is interesting and the paper contains publishable materials.
However, the reviewer has the following comments:
Comment 1: The authors should emphasize the merits of the developed method.
Comment 2: In the section simulation results, the proposed approach should compare with other relevant algorithms. The authors are asked to further provide comparisons to better show the advantages of their approach.
Comment 3: The literature review is not good enough .
Comment 4: The reviewer strongly recommends authors to experimentally verify the theoretical results to increase the impact of the paper.
Comment 5: Some minor grammatical errors should be eliminated. The authors are kindly asked to double check the manuscript.
Comment 6. The Abstract could be more concise and to the point.
Comment 7 I suggest the authors consider exposes the equations more clearly so to achieve a broader audience.
Comment 8 Please add more sentences to describe the limitations of this work. The advantages and disadvantages should be discussed.
Comment 9. I would like to see positive answers to these comments.
Author Response
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