Novel Admissibility Criteria and Multiple Simulations for Descriptor Fractional Order Systems with Minimal LMI Variables
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsReport on “Novel Admissibility Criteria and Multi Simulations for Descriptor Fractional Order Systems with Minimal LMI Variable“, by Xinhai Wang and Jin-Xi Zhang, submitted for a possible publication in Fractal and Fractional.
In this paper, the authors investigated the admissibility criteria, without eigenvalues on the boundary axes, for descriptor fractional order systems whose order belongs to (0,2). Moreover, they provided a unified admissibility criterion for the indicated class is involving with the minimal linear matrix inequality variable. Appropriate numerical simulations of the anti-symmetric matrix in the stability criteria for the system are presented together with chosen examples.
This is a nice piece of paper, its results are accurate, interesting and applicable. I suggest accepting it for publication after the following minor changes done.
1/ System (1) is named as “unforced descriptor fractional order system”. What does mean “unforced descriptor”? is the kernel of $E$ different than zero? What’s the difference between this type and “degenerate fractional order system”? some preliminaries should be included.
2/ The order of Caputo derivative chosen to be in (0, 2), this is unusual!! If your work is a generalization for 1st order system, then here the order should be in (0, 1] and one initial condition is needed for the solvability. If your work is a generalization for 2nd order system, then here the order should be in (1, 2] and two initial conditions are needed for the solvability. Check this issue.
3/ Page 4, line 125, it is mentioned Lemma 5, please correct since it is not stated.
4/ What kind of stability you have used in Theorem 1?
5/ In Theorem 2, the order should be in (1, 2] not [1, 2). Check the rest of paper. Generalization of nth order “n” is an order belongs to (n-1, n].
Comments on the Quality of English Language
Can be improved.
Author Response
Please see the attached PDF file.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsReport on manuscript
Novel Admissibility Criteria and Multi Simulations for
Descriptor Fractional Order Systems with Minimal LMI Variable
by
Xinhai Wang and Jin-Xi Zhang
· Overview of manuscript
The authors present simulations of an anti-symmetric matrix to understand the stability of fractional order systems (FOS). It then explores criteria for descriptor fractional order systems (DFOS) with orders between 0 and 2, ensuring they meet specific admissibility conditions. Finally, numerical examples are given to validate the findings, which are based on linear matrix inequality (LMI).
· Comments on text
1. New contribution
The authors need to add few words about the new contribution of their work.
2. English
The English in this paper is good.
Comments
The authors provided sufficient analysis to support their findings; however, they may consider elaborating on the following areas as future work for their study:
a) That would be great if the authors could discuss a bit about how the stability criteria for fractional order systems can be applied to more complex real-world systems.
b) That would be great if the authors could discuss a bit about new methods for simplifying the linear matrix inequality (LMI) conditions to make the analysis of descriptor fractional order systems easier.
c) That would be great if the authors can discuss a bit about developing new algorithms to automate the analysis of admissibility criteria for different types of fractional order systems.
d) That would be great if the authors could discuss a bit about extending their study to include fractional order systems with eigenvalues on the boundary axes to broaden the applicability of the findings.
· Recommendation
After all the revisions, I can recommend acceptance of this paper.
Author Response
Please see the attached PDF file.
Author Response File: Author Response.pdf
