MATLAB CONTROL SYSTEM TOOLBOX 9 User's Guide download pdf (Page 419)

100

101

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)

Ric X() A

XXAXBB

X– Q++0==

ABB

X–

Ric X

()

ABB

X–

Ric X

()

---------------------------=

Ric X() A

XE E

XA E

XB S+()R

–

XE S

+()– Q++0==

–

XE S

+()=

∞

–

1 2 ... 414 415 416 417 418 419 420 421 422 423 424 ... 648 649

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MATLAB CONTROL SYSTEM TOOLBOX 9 User's Guide Page 419

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