Hi people

I am following a course on control theory, but I got stuck on the following problem

In my book, it is given that (s / [(s-a)(s-a*)]) can be realized in
state-space as

sX(s) =AX(s)+BU(s) Y(s) =CX(s)

(provided that X is a vector of 2 states)

with

A = [ Real(a) Real(a)-abs(a) ; Real(a)+abs(a) Real(a) ]; B = [ 1 ; 1 ]; C = [ 1 1 ];

I know this representation is not unique, but I don't understand how to obtain it. I found a book how I can realize the transfer function in companion form (or e.g. with A diagonal matrix), but then A has a different structure.

Can someone enlighten me here, how they found the A,B,C matrix in this form?

Thanks Robert

I am following a course on control theory, but I got stuck on the following problem

In my book, it is given that (s / [(s-a)(s-a*)]) can be realized in

sX(s) =AX(s)+BU(s) Y(s) =CX(s)

(provided that X is a vector of 2 states)

with

A = [ Real(a) Real(a)-abs(a) ; Real(a)+abs(a) Real(a) ]; B = [ 1 ; 1 ]; C = [ 1 1 ];

I know this representation is not unique, but I don't understand how to obtain it. I found a book how I can realize the transfer function in companion form (or e.g. with A diagonal matrix), but then A has a different structure.

Can someone enlighten me here, how they found the A,B,C matrix in this form?

Thanks Robert