Hello,
To compute the frequency response of a linear system
\dot{x} = Ax + Bu
y = Cx
where A is a square matrix, one should compute G(s) = C(sI - A)\backslash B for several complex values s.
This can be done efficiently [1] with a Hessenberg factorization A = QHQ^*, since then
G(s) = CQ(sI - H)\backslash (Q^*B), where (sI - H) is Hessenberg.
There is the LinearAlgebra.Hessenberg object but I can’t find any method for an efficient \ with the Hessenberg matrix that it contains. I guess I’m missing something? Thanks
[1] Laub, Alan. “Efficient multivariable frequency response computations.” IEEE Transactions on Automatic Control 26.2 (1981)