Mohsin
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 Aug1 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!! Aug1 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 Aug1 awarded Commentator Aug1 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. Jul31 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. Jul31 asked Controllability and observability of a transfer function Jul13 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 :( Jul13 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} Jul13 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} Jul13 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 Jul13 asked Eigen value of a complex block matrix Jul11 asked Eigenvalue of 'extended block' matrix Jul11 comment Eigen value of a block matrix Thanks for the answer, i have got the point :) Jul10 awarded Student Jul10 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. Jul10 asked Eigen value of a block matrix