User`s guide

care
11-29
11care
Purpose Solve continuous-time algebraic Riccati equations (CARE)
Syntax [X,L,G,rr] = care(A,B,Q)
[X,L,G,rr] = care(A,B,Q,R,S,E)
[X,L,G,report] = care(A,B,Q,...,'report')
[X1,X2,L,report] = care(A,B,Q,...,'implicit')
Description [X,L,G,rr] = care(A,B,Q) computes the unique solution of the algebraic
Riccati equation
such that has all its eigenvalues in the open left-half plane. The
matrix is symmetric and called the stabilizing solution of .
[X,L,G,rr] = care(A,B,Q) also returns:
• The eigenvalues
L of
• The gain matrix
• The relative residual rr defined by
[X,L,G,rr] = care(A,B,Q,R,S,E) solves the more general Riccati equation
Here the gain matrix is
and the “closed-loop”
eigenvalues are
L = eig(A–B*G,E).
Two additional syntaxes are provided to help develop applications such as
-optimal control design.
[X,L,G,report] = care(A,B,Q,...,'report')turns off the error messages
when the solution fails to exist and returns a failure re port instead.
The value of
report is:
•
–1 when the associated Hamiltonian pencil has eigenvalues on or very near
the imaginary axis (failure)
•
–2 when there is no finite solution, i.e., with singular
(failure)
• The relative residual defined above when the solution exists (success)
X
Ric X() A
T
XXAXBB
T
X– Q++0==
ABB
T
X–
X
Ric X
()
0
=
ABB
T
X–
GB
T
X=
rr
Ric X
()
F
X
F
---------------------------=
Ric X() A
T
XE E
T
XA E
T
XB S+()R
1
–
B
T
XE S
T
+()– Q++0==
GR
1
–
B
T
XE S
T
+()=
H
∞
X
XX
2
X
1
1
–
=
X
1
rr