Specifications

care
16-32
16care
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
• Therelativeresidualrr 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 report 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)
X
Ric X
()
A
T
XXAXBB
T
X– Q++0==
ABB
T
X–
XRicX
()
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