File: gcare.man

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