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.TH ric_desc 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
ric_desc - Riccati equation
.SH CALLING SEQUENCE
.nf
X=ric_desc(H [,E))
[X1,X2,zero]=ric_desc(H [,E])
.fi
.SH PARAMETERS
.TP 12
H,E
: real square matrices
.TP
X1,X2
: real square matrices
.TP
zero
: real number
.SH DESCRIPTION
Riccati solver with hamiltonian matrices as inputs.
.LP
In the continuous time case calling sequence is (one input):
.Vb ric_descr(H)
.LP
Riccati equation is:
.nf
(Ec) A'*X + X*A + X*R*X -Q = 0.
.fi
Defining the hamiltonian matrix \fVH\fR by:
.nf
H = [A R;
Q -A']
.fi
with the calling sequence \fV[X1,X2,zero]=ric_descr(H)\fR, the
solution \fVX\fR is given by \fVX=X1/X2\fR.
.LP
\fVzero\fR = L1 norm of rhs of (\fVEc\fR)
.LP
The solution \fVX\fR is also given by \fVX=riccati(A,Q,R,'c'))\fR
.LP
In the discrete-time case calling sequence is (two inputs):
.Vb ric_descr(H,E)
.LP
The Riccati equation is:
.nf
(Ed) A'*X*A-(A'*X*B*(R+B'*X*B)^-1)*(B'*X*A)+C-X = 0.
.fi
Defining \fVG=B/R*B'\fR and the hamiltonian pencil \fV(E,H)\fR by:
.nf
E=[eye(n,n),G; H=[A, 0*ones(n,n);
0*ones(n,n),A'] -C, eye(n,n)];
.fi
with the calling sequence \fV[X1,X2,err]=ric_descr(H,E)\fR, the
solution \fVX\fR is given by \fVX=X1/X2\fR.
.LP
\fVzero\fR= L1 norm of rhs of (\fVEd\fR)
.LP
The solution \fVX\fR is also given by \fVX=riccati(A,G,C,'d')\fR
with \fVG=B/R*B'\fR
.SH SEE ALSO
riccati
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