User`s guide

Table Of Contents

dare

11-55

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 e rror messages

when the solution fails to exist and returns a failure re port instead. T he

value of

report is:

•

–1 whentheassociatedsymplecticpencilhaseigenvaluesonorverynear the

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 w hen 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

subs pace.

Limitations The pair must be stabilizable (that is, all eigenvalues of outside the

unit disk must be controllable). In addition, the associated symplectic pencil

musthave no eigenvalueon the unit circle.Sufficient conditionsfor this tohold

are detectable when and , or

See Also care Solve continuous-time Riccati equations

dlyap S olv e discrete-time Lyapunov equations

∞

–

,()