User`s guide

care
11-31
Finally, note that the variable l contains the closed-loop eigenvalues eig(a–
b*g)
.
l
l =
–3.5026
–1.4370
Example 2
To solve the -like Riccati equation
rewrite it in the
care format as
You can now compute the stabilizing solution by
B = [B1 , B2]
m1 = size(B1,2)
m2 = size(B2,2)
R = [–g^2*eye(m1) zeros(m1,m2) ; zeros(m2,m1) eye(m2)]
X = care(A,B,C'*C,R)
Algorithm care implements the algorithms described in [1]. It works with the
Hamiltonian matrix when is well-conditioned and ; otherwise it uses
the extended Hamiltonian pencil and QZ algorithm.
Limitations The pair must be stabilizable (that is, all unstable modes are
controllable). In addition, the associated Hamiltonian matrix or pencil must
have no eigenvalue on the imaginary axis. Sufficient conditions for this to hold
are detectable when and , or
H
∞
A
T
XXAXγ
2
–
B
1
B
1
T
B
2
B
2
T
–()X++ C
T
C+ 0=
A
T
XXAXB
1
B
2
,[]
γ
2–
I–0
0I
1–
B
1
T
B
2
T
X– C
T
C++0=
B
R
    
    
X
R
EI
=
AB
,()
QA
,()
S0
=
R0
>