About the necessary and sufficient condition for the robust Hurwitz and Schur stability of interval matrices [closed]

By relying on a two-dimensional (2-D) face test, Ref [1,2] obtained a necessary and sufficient condition for the robust Hurwitz and Schur stability of interval matrices.Ref [1,2] revealed that it is impossible that there are some isolated unstable points in the parameter space of the matrix family, so the stability of exposed 2-D faces of an interval matrix guarantees stability of the matrix family.

Ref [1,2] provides the examples to demonstrate the applicability of the robust stability test of interval matrices. Remarks:

1. The 2-D face of an interval matrix is Hurwitz stable, if and only if the maximum real part of the eigenvalues of the 2-D face of the interval matrix is smaller than 0 [1].
2. An interval matrix is Hurwitz stable, if and only if all the 2-D faces of the interval matrix is Hurwitz stable.
3. The 2-D face of an interval matrix is Schur stable, if and only if the maximum absolute of the eigenvalues of all the 2-D faces of the interval matrix is smaller than 1 [1].
4. An interval matrix is Schur stable, if and only if all the 2-D face of the interval matrix is Schur stable.
5. To determine the stability of interval matrix, needs to test all the 2-D faces of matrices.

Refs:

[1] Yang Xiao; Unbehauen, R., Robust Hurwitz and Schur stability test for interval matrices, Proceedings of the 39th IEEE Conference on Decision and Control, 2000. Volume 5, Page(s):4209 – 4214. The paper [1] can be downloaded from Web site of IEEE Explore.

[2] XIAO Yang, Stability Analysis of Multidimensional Systems, Shanghai Science and Technology Press, Shanghai, 2003.

Now, I hope that someone can discuss or comment the results of [1].

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Dear Yang Xiao: It looks like you just did a fantastic job discussing and commenting your results. I'm afraid I have to close this as 'not a real question' since there is no question anywhere. You may want to read mathoverflow.net/faq#whatquestions and mathoverflow.net/howtoask to see how to ask a question on MO. When you edit your question to fit our guidelines, flag for moderator attention to reopen it. – François G. Dorais Aug 28 2011 at 13:20
Maybe the OP wanted to remark on this question: mathoverflow.net/questions/58701/… But then, he/she did not understand that particular question, which is not about matrix functions but only one single matrix. – András Bátkai Aug 28 2011 at 20:35