File: gfare.man

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.TH gfare 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
gfare - filter Riccati equation
.SH CALLING SEQUENCE
.nf
[Z,H]=gfare(Sl)
.fi
.SH PARAMETERS
.TP 8
Sl
: linear system (\fVsyslin\fR list)
.TP
Z
: symmetric matrix
.TP
H
: real matrix
.SH DESCRIPTION
Generalized Filter Algebraic Riccati Equation (GFARE).
\fVZ\fR = solution, \fVH\fR = gain.
.LP
The GFARE for \fVSl=[A,B,C,D]\fR is:
.nf
(A-B*D'*Ri*C)*Z+Z*(A-B*D'*Ri*C)'-Z*C'*Ri*C*Z+B*Si*B'=0
.fi
where \fVS=(eye+D'*D)\fR, \fVSi=inv(S)\fR, \fVR=(eye+D*D')\fR, \fVRi=inv(R)\fR
and \fVH=-(B*D'+Z*C')*Ri\fR is such that \fVA+H*C\fR is stable.
.SH SEE ALSO
gcare