Controllability matrix computation for time invariant linear system without using built in ctrb function.

Controllability matrix C = [B,A*B,...,A^(n-1)*B], where A is n x n matrix and B is n x m matrix.

I would like to compute C without using ctrb function. I was thinking of calculating all the matrices i.e. B,A*B,...,A^(n-1)*B and then concatenating them together using cat function. Maybe using a for loop to do so. I know it would not be efficient. However, i would still like to give it a go. Any suggestions or different approaches would be helpful.

Answer 1

[Matt J]

I would use the fact that C{i}=A*C{i-1}.