Axiomatic Foundations of Anisotropy-Based and Spectral Entropy Analysis: A Comparative Study

Round 1

Reviewer 1 Report

The paper is well organized and written. It provides an overview of two different axiomatic approaches in control theory, namely anisotropy-based and spectral entropy-based approaches. The main goal of the paper is to compare these two methods and discuss their applications. The reviewer has the following remarks about the presented work.

1.     In the introduction, the literature cited is relatively small and the analysis of the current state of research is not comprehensive. It is suggested that some references from the last three years be added and reviewed in the introduction.

2.     In the derivation section, each symbol should be defined and given an explanation, and authors are advised to check and interpret the symbols.

3.     There is no simulation or experimental validation in this paper. Is it convincing? Additional simulations or experimental validation are recommended.

4.     Formatting and grammar problems in the text should be corrected.

Formatting and grammar problems in the text should be corrected.

Author Response

Thank you for your valuable comments, that helped us to improve the paper. Please, find the answers in the attached file.

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper is a comparative study. Two approaches, the theory based on anisotropy and the spectral entropy approach, are discussed and their respective ranges, advantages and disadvantages are presented. The methods are sound, the ideas clear, and the conclusions clear. This is a really interesting piece of research. No obvious problems were found and the publication was recommended.

Author Response

Thank you for your valuable comments, that helped us to improve the paper. Please, find the answers in the attached file.

Author Response File: Author Response.pdf

Reviewer 3 Report

My comments to the authors are attached.

From my point of view, the paper is interesting, the conclusions seem mathematically correct. I recommend minor revision.

Comments for author File: Comments.pdf

Author Response

Thank you for your valuable comments, that helped us to improve the paper. Please, find the answers in the attached file.

Author Response File: Author Response.pdf

Reviewer 4 Report

In my opinion, the paper is well written and organized. The work of the paper is correct. Howevr,there 

are some comments to improve the quality of the paper which are given as follows: 

 

1.What are the key contributions of the results of this paper to the problem of interest? In the introduction part, the author should give more background works in details about advantages of the proposed method over the existing methods.

(2) Some remarks on the computation complexity of the obtained results should be given. 

(3) for the considered model (10) ? A remark is suggested to be added. 

(4)What are the novelties of the methods and techniques used in the paper leading the claimed results? For example, what is the novelty in the construction of e definition of σ-entropygain or what is the creation of the controllers? Some description or remarks should be given.

(5) In Equation (13, Is possible to value is 2 or general?

There are some grammatical and clerical errors in the manuscript.

Author Response

Thank you for your valuable comments, that helped us to improve the paper. Please, find the answers in the attached file.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

I have no further comments.