Finite-Time Stabilization for Stochastic Interval Systems with Time Delay and Application to Energy-Storing Electrical Circuits

Round 1

Reviewer 1 Report

-          What is newly proposed for stochastic interval systems with time delay in this paper? It is not clearly mentioned.

-          What is improved for energy-storing electrical circuits by applying the proposed method?

-           Further investigation is required for energy-storing electrical circuits with stochastic interval systems in the introduction.

-       In equation (10), the definition of  is omitted. Please, add the definition of .

Author Response

Comment 1: What is newly proposed for stochastic interval systems with time delay in this paper? It is not clearly mentioned.

Response: Thanks for your valuable comment. In the revised manuscript, we have clearly mentioned the newly proposed results on stochastic interval systems with time delay. See “However, it's not difficult to find that the existing results mainly focus on the finite-time dissipative control for stochastic interval systems with time delay, or Lyapunov stability of stochastic systems with time delay. To the best of our knowledge, the problems of finite-time stability for stochastic delay interval systems have not been fully considered, which motivates this study.”

Comment 2: What is improved for energy-storing electrical circuits by applying the proposed method?

Response: Thanks for your comment. In the revised manuscript, we have explained the improvement for energy-storing electrical circuits by applying the proposed method. See “Finally, the proposed method is applied to an energy-storing electrical circuit to demonstrate that the designed controller is effective to stabilize the energy-storing electrical circuit in finite-time. Undoubtedly, not only the error of electronic components but also the stochastic disturbance of energy-storing electrical circuit model proposed in this paper are considered, which mean the model proposed in this paper is more accurate and the proposed method is with very good robustness.”

Comment 3: Further investigation is required for energy-storing electrical circuits with stochastic interval systems in the introduction.

Response: Thanks for your advice. In the revised manuscript we have added the further investigations for energy-storing electrical circuits in the introduction. See “Meanwhile, more and more important applications of energy-storing electrical circuits go everywhere in our lives and in industrial production. Up to now, a lot of investigations on the energy-storing electrical circuits have been published, for example, finite-time control [36], stability [37] and passivity [38, 39]. However, in the exist results of energy-storing electrical circuits, the stochastic disturbance is not considered, and the values of electronic components are exact. It is almost impossible in practical energy-storing electrical circuits.”

Comment 4: In equation (10), the definition of is omitted. Please, add the definition of.

Response: Thanks for your careful reading. We have added lemma 4 as the definition of $It\hat{o}$ formula.

Author Response File: Author Response.pdf

Reviewer 2 Report

Reviewer : The authors of this paper investigated the finite-time stabilization for stochastic time-delay systems with parameter uncertainties via nonlinear feedback controller. The topic of the paper is interesting. This paper is generally well organized, and the proof of the main results is seemingly correct.  However, the authors fix the following issues before submitting the final version of the paper.

1.     How to design $bar{K}$ and $hat{K}$? The authors should explain clearly in Theorems. Further, the value of  gains $bar{K}$ and $hat{K}$ should be provided.

2.     The advantages of the proposed method or the results of this paper should be more highlighted. More discussion about the effectiveness of the proposed approach should be strengthened that show the advantages of the proposed scheme.

3.     Some typos and corrections are found in the manuscript. Please correct and check all the probable typos, errors and mistakes carefully.

4.     Conclusion needs to have more discussion.

5.     Check the reference part thoroughly and update all references.

6.    Some related references can be added to explain the background of this research such as Communications in Nonlinear Science and Numerical Simulation, Vol.68, pp. 203-219, March 2019; Journal of the Franklin Institute, Vol.355, pp. 6531-6548, Sep. 2018;Neural Networks, Vol. 106, October 2018, pp 67-78;Applied Mathematics Letter, Vol.77, pp. 6-12, March 1st 2017.

Author Response

Comment 1:How to design $bar{K}$ and $hat{K}$? The authors should explain clearly in Theorems. Further, the value of gains $bar{K}$ and $hat{K}$ should be provided.

Response: Thanks for your valuable comment. The three controller gains$K,\bar{K}, \hat{K}$ are explained in Remark 1. To explain how to design $\bar{K}$ and $\hat{K}$, we give an algorithm in Remark 4. Further, the value of gains $\bar{K}$ and $\hat{K}$ also have been provided in section 4.2.

Comment2: The advantages of the proposed method or the results of this paper should be more highlighted. More discussion about the effectiveness of the proposed approach should be strengthened that show the advantages of the proposed scheme.

Response: Thanks for your suggestion. In the revised manuscript, we have many times highlighted the advantages of the proposed method or the results of this paper in introduction, in remark 1 and 3, and in conclusions respectively.Of course, more discussion about the effectiveness of the proposed approach also has been strengthened in simulations.

Comment 3: Some typos and corrections are found in the manuscript. Please correct and check all the probable typos, errors and mistakes carefully.

Response: Thanks for your careful reading. The revised manuscript has beenchecked carefully and the improper English expressions have been corrected.

Comment 4: Conclusion needs to have more discussion.

Response: Thanks for your good suggestion. In revised manuscript more discussions have been done in conclusions.

Comment5: Check the reference part thoroughly and update all references.

Response: Thanks for your comment. The references of revised manuscript has been checked thoroughly and updated.

Comment6:Some related references can be added to explain the background of this research such as Communications in Nonlinear Science and Numerical Simulation, Vol.68, pp. 203-219, March 2019; Journal of the Franklin Institute, Vol.355, pp. 6531-6548, Sep. 2018;Neural Networks, Vol. 106, October 2018, pp 67-78;Applied Mathematics Letter, Vol.77, pp. 6-12, March 1st 2017.

Response: Thanks for your comment.Some related references including what you mentioned have been added in the revised manuscript.

Author Response File: Author Response.pdf