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seen Oct 15 '12 at 18:06

Aug
1
comment Controllability and observability of a transfer function
the order of ss model is 20, but it's not minimal. The rank of controllability gramian = 20 while the rank of observability gramian = 10. which is strange!!
Aug
1
comment Controllability and observability of a transfer function
both (s+10)^10 and (s+0.8)^10 are in the denominator, hence the order is 20. Numerator is just 1
Aug
1
awarded  Commentator
Aug
1
comment Controllability and observability of a transfer function
Sorry i mis-interpret your message, both (s+10)^10 and (s+0.8)^10 are in the denominator, hence the order is 20. Numerator is just 1.
Jul
31
comment Controllability and observability of a transfer function
Indeed!! and also the rank of observability matrix. The one you mentioned is controllablity matrix. The question is that why the rank of these matrices are less than the order of the system, which is 20 in this case? when there is no pole zero cancellation.
Jul
31
asked Controllability and observability of a transfer function
Jul
23
comment H infinity norm of error dynamics
sys and sys1 are SISO systems, while all the system matrices have appropriate dimensions.
Jul
23
asked H infinity norm of error dynamics
Jul
13
comment Eigen values of sum of two matrices
I am unable to find such S. I can find an S such that SM_bS^-1 is just M_b with the change of signs as i am mentioning. Another important thing i want to mention is for M_b the rank of \begin{pmatrix}c^\top c&-c^\top c\\-cr^\top c&cr^\top c\end{pmatrix} is always 1.
Jul
13
asked Eigen values of sum of two matrices
Jul
13
comment Eigen value of a complex block matrix
Now the problem is with the signs of 'c^\top c_r' and 'c_r^\top c' as they change their signs the eigen values doesn't change. what will be the effect of this on the whole M1... this is my question. I hope that i am able to put my question correctly. I feel extremely sorry for this mess of comments :(
Jul
13
comment Eigen value of a complex block matrix
I am new here, unable to type the problem correctly. The second matrix in the sum is \begin{pmatrix} c^\top c&-c^\top c_r&0\\-c_r^\top c&c_r^\top c_r&0\\0&0&I \end{pmatrix}
Jul
13
comment Eigen value of a complex block matrix
its like &M1& \begin{align}\begin{pmatrix}a_{11}&0&b_{13}\\0&a_{22}&b_{23}\\b_{13}^\top &b_{23}^\top&d_{33}\end{pmatrix} + \begin{pmatrix}c^\top c &-cc_r&0\\-c_r c&c_rc_r&0\\0 &0 &I\end{pmatrix} \end{align}
Jul
13
comment Eigen value of a complex block matrix
Thanks for the reply, you can understand it like there is a M1 which is the sum of two matrices e.g., M1 = Ma + Mb. Now for Mb matrix the eigen values doesn't change with changing signs of cr (i can prove this by using a similar matrix technique which P = [I 0 0;0 -I 0;0 0 I] where I is the identity matrix of appropriate dimension... Now the question is that what will be the net effect of no change of eigen value of Mb on M1? I hope it clearfy the question a bit
Jul
13
asked Eigen value of a complex block matrix
Jul
11
answered Eigenvalue of 'extended block' matrix
Jul
11
asked Eigenvalue of 'extended block' matrix
Jul
11
comment Eigen value of a block matrix
Thanks for the answer, i have got the point :)
Jul
10
awarded  Student
Jul
10
comment Eigen value of a block matrix
I didn't get what you ask me do? M1 and M2 are real block matrices, with appropriate dimensions of A, B and D.