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I have a question about similarity transform, with regard to the state space formulation of a dynamical system.

Given a system (A,B,C,D) with minimal realization but written on an arbitrary form, is there a (fairly simple) way of finding the similarity transformation that transforms the system matrices to a specified structure? For example, find the similarity transformation that transforms:

A = [a11 a12 a13;

a21 a22 a23;

a31 a32 a33];

B = [b1; b2; b3];

C = [c1 c2 c3];

D = d;

into

Á = [á11 á12 á13;

-á21 0 á21;

0 á32 -á32];

B´ = [0; 0;b´];

C´ = [0 á32 -á32];

D´ = b´;

Where the ´ just distinguishes the transformed matrices/elements from the original ones. This was just an example, but I hope you get the gist of it! If it's avoidable, the algebraic expressions of one entry in terms of the others aren't of interest. Only numerical matrices will be used, but the result should be of the above structure. I imagine this is an inherently tricky problem, but I just wanted to make sure I hadn't neglected anything obvious.

Thanks so much in advance!

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# Similarity Transform with specifications

Can you offer guidance or do you also need help?

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