Switched Observer Design for a Class of Non-Linear Systems

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper deals with switched observer design for a class of nonlinear systems. By transforming the error system into an LPV system, some sufficient conditions are obtained for stability and the existence of observer gains. A numerical example is given to show the effectiveness of the proposed results. Below are some comments:

1.        In the first paragraph of Introduction, some results on Luenberger-type state observers should be mentioned, e.g. “State estimation for static neural networks with time-varying delays based on an improved reciprocally convex inequality” and “Sufficient conditions for a class of matrix-valued polynomial inequalities on closed intervals and application to H∞ filtering for linear systems with time-varying delays”. 

2.        On line 16, what is the conservatism referred to? More explanation on conservatism is needed.

3.        On line 90, is the model (2) from some practical engineering applications? Why is not the term Ax(t) merged to the nonlinear function f(x(t))?

4.        On line 97, what is the motivation of such a switched state observer (3)? This point should be enhanced.

5.        The proofs seem correct. Some remarks should be added in the paper to highlight the novelties and contributions.

6.        Please double check the paper.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper studied the switched observer design for a class of nonlinear systems. An uncertain polytopic linear equivalent model for the estimate error dynamics equations is obtained, and sufficient conditions for the existence of a switching output injection gain are proposed such that the asymptotic stability of the estimation error is guaranteed. Finally, simulation results are given to support the analytical results presented in this paper. When preparing the revised paper, the following points need to be clarified:

1.       The literature review is quite brief and needs to be more comprehensive. Please expand on the existing research to provide a better background for your work.

2.       The main challenge of this paper compared to the existing literature should be further emphasized. More explanations are preferred to highlight the technique difficulty on the study.

3.       Some abbreviations should be explained when first appearing, e.g., “SDP” in line 42 on page 2.

4.       Some denotations need clear explanations, e.g., "D^+" in Eq (20) on page 6.

5.       The format of the references should be uniformly. For example, [3], [7], [18], [20] are not standard.

6.       Some typos should be double checked throughout the paper, such as,

(1) "." in line 74 on page 3 should be ";"

(2) “Figure 1:-- Figure 5:” should be consistent in format.

 

Comments on the Quality of English Language

This paper studied the switched observer design for a class of nonlinear systems. An uncertain polytopic linear equivalent model for the estimate error dynamics equations is obtained, and sufficient conditions for the existence of a switching output injection gain are proposed such that the asymptotic stability of the estimation error is guaranteed. Finally, simulation results are given to support the analytical results presented in this paper. When preparing the revised paper, the following points need to be clarified:

1.       The literature review is quite brief and needs to be more comprehensive. Please expand on the existing research to provide a better background for your work.

2.       The main challenge of this paper compared to the existing literature should be further emphasized. More explanations are preferred to highlight the technique difficulty on the study.

3.       Some abbreviations should be explained when first appearing, e.g., “SDP” in line 42 on page 2.

4.       Some denotations need clear explanations, e.g., "D^+" in Eq (20) on page 6.

5.       The format of the references should be uniformly. For example, [3], [7], [18], [20] are not standard.

6.       Some typos should be double checked throughout the paper, such as,

(1) "." in line 74 on page 3 should be ";"

(2) “Figure 1:-- Figure 5:” should be consistent in format

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Dear authors,

The paper must be improved according to the comments in the attached document.  

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

No further comments.

Author Response

Comments 1: No further comments.

Response 1: We would like to thank Reviewer 1 for the positive evaluation of the paper.

Reviewer 3 Report

Comments and Suggestions for Authors

Dear authors,

I accept the paper in its present form. 

However, in line 323 there is a [?], what is a mistake. This must be corrected. 

 

Author Response

Comments 1:  I accept the paper in its present form.  However, in line 323 there is a [?], what is a mistake. This must be corrected. 

Response 1: We would like to thank the Associate editor for the positive evaluation of the paper. We have corrected the referred mistake.