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.TH H_inf 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
h_inf - H-infinity (central) controller
.SH CALLING SEQUENCE
.nf
[Sk,ro]=h_inf(P,r,romin,romax,nmax)
[Sk,rk,ro]=h_inf(P,r,romin,romax,nmax)
.fi
.SH PARAMETERS
.TP 15
P
: \fVsyslin\fR list : continuous-time linear system (``augmented'' plant given in state-space form
or in transfer form)
.TP
r
: size of the \fVP22\fR plant i.e. 2-vector [#outputs,#inputs]
.TP
romin,romax
: a priori bounds on \fVro\fR with \fVro=1/gama^2\fR; (\fVromin=0\fR usually)
.TP
nmax
: integer, maximum number of iterations in the gama-iteration.
.SH DESCRIPTION
\fVh_inf\fR computes H-infinity optimal controller for the
continuous-time plant \fVP\fR.
.LP
The partition of \fVP\fR into four sub-plants is given through
the 2-vector \fVr\fR which is the size of the \fV22\fR part of \fVP\fR.
.LP
\fVP\fR is given in state-space
e.g. \fVP=syslin('c',A,B,C,D)\fR with \fVA,B,C,D\fR = constant matrices
or \fVP=syslin('c',H)\fR with \fVH\fR a transfer matrix.
.LP
.Vb [Sk,ro]=H_inf(P,r,romin,romax,nmax)
returns \fVro\fR in \fV[romin,romax]\fR and the central controller
\fVSk\fR in the same representation as \fVP\fR.
.LP
(All calculations are made in state-space, i.e conversion to state-space
is done by the function, if necessary).
.LP
Invoked with three LHS parameters,
.Vb [Sk,rk,ro]=H_inf(P,r,romin,romax,nmax)
returns \fVro\fR and the Parameterization of all stabilizing
controllers:
.LP
a stabilizing controller \fVK\fR is obtained by
\fVK=lft(Sk,r,PHI)\fR where \fVPHI\fR is a linear system with
dimensions \fVr'\fR and satisfy:
.LP
\fVH_norm(PHI) < gamma\fR.
\fVrk (=r)\fR is the size of the \fVSk22\fR block and \fVro = 1/gama^2\fR
after \fVnmax\fR iterations.
.LP
Algorithm is adapted from Safonov-Limebeer. Note that \fVP\fR is assumed to be
a continuous-time plant.
.SH SEE ALSO
gamitg, ccontrg, leqr
.SH AUTHOR
F.D. (1990)
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