User`s guide

canon
11-28
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 sta te 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 o f 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
sufficientconditionfor diagonalizability is that hasno repeated eigenvalues.
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. L inear Systems, Prentice-Hall, 1980.
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x
c
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c
Tx
=
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A
x
c
·
P
1
–
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c
P
1
–
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c
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P
A
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