User`s guide

dare
11-54
11dare
Purpose Solve discrete-time algebraic Riccati equations (DARE)
Syntax [X,L,G,rr] = dare(A,B,Q,R)
[X,L,G,rr] = dare(A,B,Q,R,S,E)
[X,L,G,report] = dare(A,B,Q,...,'report')
[X1,X2,L,report] = dare(A,B,Q,...,'implicit')
Description [X,L,G,rr] = dare(A,B,Q,R) computes the unique solution of the
discrete-time algebraic Riccati equation
such that the “closed-loop” matrix
has all its eigenvalues inside the unit disk. The matrix is symmetric and
called the stabilizing solution of .
[X,L,G,rr] = dare(A,B,Q,R)
also returns:
• The eigenvalues
L of
• The gain ma trix
• Therelativeresidual
rr defined by
[X,L,G,rr] = dare(A,B,Q,R,S,E) solves the more general DARE:
The corresponding gain matrix and closed-loop eigenvalues are
X
Ric X() A
T
XA X– A
T
XB B
T
XB R+()
1
–
B
T
XA– Q+ 0==
A
cl
ABB
T
XB R+()
1
–
B
T
XA–=
X
Ric X
()
0
=
A
cl
GB
T
XB R+()
1
–
B
T
XA=
rr
Ric X
()
F
X
F
---------------------------=
A
T
XA E
T
XE– A
T
XB S+()B
T
XB R+()
1
–
B
T
XA S
T
+()– Q+0=
GB
T
XB R+()
1
–
B
T
XA S
T
+()=