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Rosenbrock system matrix : ウィキペディア英語版
Rosenbrock system matrix

The Rosenbrock System Matrix (or Rosenbrock's system matrix) of a linear time invariant system is a useful representation bridging state-space representation and transfer function matrix form. It was proposed in 1967 by Howard H. Rosenbrock.
== Definition ==

Consider the dynamic system
:: \dot= Ax +Bu,
:: y= Cx +Du.
The Rosenbrock system matrix is given by
::P(s)=\begin
sI-A & -B\\
C & D
\end.
In the original work by Rosenbrock, the constant matrix D is allowed to be a polynomial in s.
The transfer function between the input i and output j is given by
::g_=\frac
\end}
where b_i is the column i of B and c_j is the row j of C.
Based in this representation, Rosenbrock developed his version of the PHB test.

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