Specifications

dare
16-56
and L = eig(A-B*G,E).
Two additional syntaxes are provided to help develop applications such as
-optimal control design.
[X,L,G,report] = dare(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 whentheassociatedsymplectic pencil haseigenvalues on orverynearthe
unit circle (failure)
•
-2 when there is no finite solution, that is, with singular
(failure)
• The relative residual defined above when the solution exists (success)
Alternatively,
[X1,X2,L,report] = dare(A,B,Q,...,'implicit') also turns
off error messages but now returns in implicit form as
Note that this syntax returns
report = 0 when successful.
Algorithm dare implements the algorithms described in [1]. It uses the QZ algorithm to
deflate the extended symplectic pencil and compute its stable invariant
subspace.
Limitations The pair must be stabilizable (that is, all eigenvalues of outside the
unit disk must be controllable). In addition, the associated symplectic pencil
must haveno eigenvalue onthe unitcircle. Sufficientconditionsfor this tohold
are detectable when and , or
See Also care Solve continuous-time Riccati equations
dlyap Solve discrete-time Lyapunov equations
H
∞
X
XX
2
X
1
1–
= X
1
rr
X
XX
2
X
1
1–
=
AB
,()
A
QA
,()
S 0= R 0
>
QS
S
T
R
0
>