@acer 
Hello Acer, I'm very glad you answer.

E is not symmetric. Matrices E,A,C,B are attached in this message.

My Riccati equations is for the descritor system: 

E.X_dot = A. X + B. U

Y = C.X

Thank you,

PS: Do you live in Kitchener-Waterloo, ON, Ca? If yes, I would like to make friend  with you and to drink coffee or beer together. 
model17_A.txt
model17_B.txt
model17_C.txt
model17_E.txt 

Hi Joe,

Thank you for your help, and sorry for my delay reply.

Maple runs your code more than 15mins but can't give the solution. I also try to use "solve", but there is no solution yet.

In addition, the matrices E and A are attached in this message.

Sincerely,
STHence
model17_A.txt   model17_E.txt 

Hi Joe,

Thank you for your help, and sorry for my delay reply.

Maple runs your code more than 15mins but can't give the solution. I also try to use "solve", but there is no solution yet.

In addition, the matrices E and A are attached in this message.

Sincerely,
STHence
model17_A.txt   model17_E.txt 

@acer : In fact, I learned some Maple functions that I had never used before, such as Digits, ImportMatrix. Your answer helps me a lot. 

I also have another question as follows:

http://www.mapleprimes.com/questions/138827-Finding-Fractorizations

Thank you and have a great weekend.

@acer : In fact, I learned some Maple functions that I had never used before, such as Digits, ImportMatrix. Your answer helps me a lot. 

I also have another question as follows:

http://www.mapleprimes.com/questions/138827-Finding-Fractorizations

Thank you and have a great weekend.

Thanks you Acer,

I found another method to find the invertible matrices S and T such that S.E.T is a square diaginal matrix. That is a singular value decomposition (SVD).

http://www.maplesoft.com/support/help/Maple/view.aspx?path=MTM/svd

Once more times, I really appreciate your help, Acer.

Thanks you Acer,

I found another method to find the invertible matrices S and T such that S.E.T is a square diaginal matrix. That is a singular value decomposition (SVD).

http://www.maplesoft.com/support/help/Maple/view.aspx?path=MTM/svd

Once more times, I really appreciate your help, Acer.

Hi Acer,

Thank you very much for your useful codes. You're a Maple expert.

As you know, the determinant of E is very small (= -1.41e-029), even though its rank is 12 (if Digits = 17). Therefore, is E singular?

1. If E is singular, how can we determine its Smith Norm Form?

2. If Digits = 10, then Rank (E) = 10. Thus, how can we determine the Smith Norm Form whose rank is equal to the rank of E?

Hi Acer,

Thank you very much for your useful codes. You're a Maple expert.

As you know, the determinant of E is very small (= -1.41e-029), even though its rank is 12 (if Digits = 17). Therefore, is E singular?

1. If E is singular, how can we determine its Smith Norm Form?

2. If Digits = 10, then Rank (E) = 10. Thus, how can we determine the Smith Norm Form whose rank is equal to the rank of E?