Specifications

canon
16-31
For state-space models sys,
[csys,T] = canon(a,b,c,d,'type')
also returns the state coordinate transformation T relating the original state
vector and the canonical state vector .
This syntax returns
T=[] when sys is not a state-space model.
Algorithm Transfer functions or zero-pole-gain models are first converted to state space
using
ss.
The transformation to modal form uses the matrix of eigenvectors of the
matrix. The modal form is then obtained as
The state transformation returned is the inverse of .
The reduction to companion form uses a state similarity transformation based
on the controllability matrix [1].
Limitations The modal transformation requires that the matrix be diagonalizable. A
sufficient conditionfordiagonalizabilityisthat has norepeatedeigenvalues.
The companion transformation requires that the system be controllable from
the first input. The companion form is often poorly conditioned for most
state-space computations; avoid using it when possible.
See Also ctrb Controllability matrix
ctrbf Controllability canonical form
ss2ss State similarity transformation
References [1] Kailath, T. Linear Systems, Prentice-Hall, 1980.
xx
c
x
c
Tx=
PA
x
c
·
P
1–
APx
c
P
1–
Bu+=
yCPx
c
Du+=
TP
A
A