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.TH stabil 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
stabil - stabilization
.SH CALLING SEQUENCE
.nf
F=stabil(A,B,alfa)
K=stabil(Sys,alfa,beta)
.fi
.SH PARAMETERS
.TP 10
A
: square real matrix (\fVnx x nx\fR)
.TP
B
: real matrix (\fVnx x nu\fR)
.TP
alfa, beta
: real or complex vector (in conjugate pairs) or real number.
.TP
F
: real matrix (\fVnx x nu\fR)
.TP
Sys
: linear system (\fVsyslin\fR list) (\fVm\fR inputs, \fVp\fR outputs).
.TP
K
: linear system (\fVp\fR inputs, \fVm\fR outputs)
.SH DESCRIPTION
\fVF=stabil(A,B,alfa)\fR returns a gain matrix \fVF\fR such that
\fVA+B*F\fR is stable if pair \fV(A,B)\fR is stabilizable.
Assignable poles are set to \fValfa(1),alfa(2),...\fR.
If \fV(A,B)\fR is not stabilizable a warning is given
and assignable poles are set to \fValfa(1),alfa(2),...\fR.
If \fValfa\fR is a number all eigenvalues are set to this
\fValfa\fR (default value is \fValfa=-1\fR).
.LP
\fVK=stabil(Sys,alfa,beta)\fR returns \fVK\fR, a compensator for \fVSys\fR
such that \fV(A,B)\fR-controllable eigenvalues are set to
\fValfa\fR and \fV(C,A)\fR-observable eigenvalues are set to \fVbeta\fR.
.LP
All assignable closed loop poles (which are given by the
eigenvalues of \fVAclosed=h_cl(Sys,K)\fR are set to \fValfa(i)\fR's
and \fVbeta(j)\fR's.
.SH EXAMPLE
.nf
// Gain:
Sys=ssrand(0,2,5,list('st',2,3,3));
A=Sys('A');B=Sys('B');F=stabil(A,B);
spec(A) //2 controllable modes 2 unstable uncontrollable modes
//and one stable uncontrollable mode
spec(A+B*F) //the two controllable modes are set to -1.
// Compensator:
Sys=ssrand(3,2,5,list('st',2,3,3)); //3 outputs, 2 inputs, 5 states
//2 controllables modes, 3 controllable or stabilizable modes.
K=stabil(Sys,-2,-3); //Compensator for Sys.
spec(Sys('A'))
spec(h_cl(Sys,K)) //K Stabilizes what can be stabilized.
.fi
.SH SEE ALSO
st_ility, contr, ppol
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