User`s guide

canon
11-27
11canon
Purpose Compute canoni cal state-space re alizations
Syntax csys = canon(sys,'type')
[csys,T] = canon(sys,'type')
Description canon computes a canonical state-space model for the continuous or discrete
LTI system
sys. Two types of canonical forms are supported.
Modal Form
csys = canon(sys,'modal') returns a realization csys in modal form, that is,
where the real eigenvalues appear on the diagonal of the matrix and the
complex conjugate eigenvalues appear in 2-by-2 blocks on the diagonal of .
For a system with eigenvalues , the modal matrix is of the
form
Companion Form
csys = canon(sys,'companion') produces a companion realization of sys
where the characteristic polynomial of the system appears explicitly in the
rightmost column of the matrix. For a system with characteristic polynomial
the corresponding companion matrix i s
A
A
λ
1
σ
j
ωλ
2
,±,()
A
λ
1
000
0σω0
0 ω– σ0
000λ
2
A
ps() s
n
a
1
s
n 1
–
... a
n 1–
sa
n
++++=
A
A
00....0a
n
–
100..0a
n1–
–
010.::
:0..::
0..10a
2
–
0....01a
1
–
=