Specifications

care
16-33
• The relative residual defined above when the solution exists (success)
Alternatively,
[X1,X2,L,report] = care(A,B,Q,...,'implicit') also turns
off error messages but now returns in implicit form.
Note that this syntax returns
report = 0 when successful.
Examples Example 1
Given
you can solve the Riccati equation
by
a = [-3 2;1 1]
b = [0 ; 1]
c = [1 -1]
r = 3
[x,l,g] = care(a,b,c'*c,r)
This yields the solution
x
x =
0.5895 1.8216
1.8216 8.8188
You can verify that this solution is indeed stabilizing by comparing the
eigenvalues of
a and a-b*g.
[eig(a) eig(a-b*g)]
ans =
rr
X
XX
2
X
1
1–
=
A
3– 2
11
= B
0
1
= C 11–= R 3=
A
T
XXAXBR
1–
B
T
X– C
T
C++0=