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The authors have addressed all of the reviewers' comments.
[# PeerJ Staff Note - this decision was reviewed and approved by Marieke Huisman, a PeerJ Computer Science Section Editor covering this Section #]
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Authors have addressed most of the concerns raised by the reviewer. The manuscript can be accepted for publication as it has significantly improved after revision.
Please make sure Reviewer 2's comments, especially regarding remark 2 are appropriately addressed.
[# PeerJ Staff Note: Please ensure that all review comments are addressed in a rebuttal letter and any edits or clarifications mentioned in the letter are also inserted into the revised manuscript where appropriate. It is a common mistake to address reviewer questions in the rebuttal letter but not in the revised manuscript. If a reviewer raised a question then your readers will probably have the same question so you should ensure that the manuscript can stand alone without the rebuttal letter. Directions on how to prepare a rebuttal letter can be found at: https://peerj.com/benefits/academic-rebuttal-letters/ #]
Authors are suggested to include more recent and relevant research, especially from the last five years to increase the knowledge base of the manuscript.
More results should be added to highlight the contributions of the manuscript.
The results should be compared with the other literature works to ensure the validity of the work.
This is an interesting work on the design of the Moving Horizon Estimator filter with the TS fuzzy controllers. The input-to-state stability is well derived for the proposed MHE. simulation runs are presented for non-Gaussian and Gaussian noises. After reading carefully, it is observed that the manuscript could be accepted with few revisions such as
1. The literature should be strengthened with recent works.
2. The contributions of the work should be clearly highlighted, preferably, point-wise before the organization of the manuscript in the 'Introduction' Section.
3. Authors should present the proper reasoning behind the selection of the Gaussian noises. There are other more critical noises such as 'speckle noise', 'Poison noise', etc.
4. The simulation results should be compared to the existing works in the literature, quantitatively or qualitatively.
5. Why the equations in Simulation and Experiments are not marked? The section 'Simulation and Experiments' should be renamed. I could not find any experiment results.
In the paper the authors proposed a filter using T-S fuzzy controllers for discrete systems. At first it is not clear what class of discrete systems they are referring to. The Abstract is somehow vague and needs improvement.
First page - please correct “ffiilter”
Section Introduction - I believe “vast” is more appropriated than “giant”
Section Introduction - I wouldn’t use “hassle” but “problem”. The colloquial use of the language should be avoided. There are several instance in the manuscript where the author made use of colloquial words where there is proper technical words to describe the same thing.
Remark 2 - The comment on MHE does not seem to solve the problem pointed out in the first sentence of the remark. So does MHE come as the solution of the problem of accurate mathematical model and sensitivity to error?
Zm,l and Wm,l are mentioned before establishing their definition.
Equation 13 - Please give References to the method and explicitly define the most common method. The reader should be able to replicate all derivations.
Just before Equation 21, it is not clear what the authors meant by “By calculation”and how they did it.
Section “Simulation and Experiments”- From my point of view, this section needs to be throughly revised. Where did the nonlinear term came from? Why L=5? What are the values of the initial conditions? And so on.
The major problem in this section is that the figures seem to contract what the authors said in the text. The authors need to explain what exactly is remarkable about the results presented in the paper. The figures showed exactly the contrary and are not convincing (std = 0.0001 - almost no noise contamination - please add a convincing noise threshold).
See above
See above
In summary, I believe that there is a potential contribution work publishing but the manuscript should undergo a second round of reviews.
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