Controllability and Observability Matrix

The controllability matrix of a statespace realisation \(k(z)=C(I-Az^{-1})^{-1}B + D\) is the matrix $$ [B,AB,\dots,A^{o-1}B] $$ and the observability matrix is $$ [C',A'C',\dots,(A')^{o-1}C']' $$

Usage

ctr_matrix(A, B, o = NULL)

obs_matrix(A, C, o = NULL)

Arguments

A

either a stsp object or a square \((s,s)\) dimensional matrix.

B

\((s,n)\) dimensional matrix. This argument is ignored if A is a stsp object.

o

(non negative) integer. The default value is \(o=s\).

C

\((m,s)\) dimensional matrix. This argument is ignored if A is a stsp object.

Value

Controllability or observability matrix.