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.TH gtild 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
gtild - tilde operation
.SH CALLING SEQUENCE
.nf
Gt=gtild(G)
Gt=gtild(G,flag)
.fi
.SH PARAMETERS
.TP 10
G
: either a polynomial or a linear system (\fVsyslin\fR list) or a rational matrix
.TP
Gt
: same as G
.TP
flag
: character string: either \fV'c'\fR or \fV'd'\fR (optional parameter).
.SH DESCRIPTION
If \fVG\fR is a polynomial matrix (or a polynomial), \fVGt=gtild(G,'c')\fR
returns the polynomial matrix \fVGt(s)=G(-s)'\fR.
.LP
If \fVG\fR is a polynomial matrix (or a polynomial), \fVGt=gtild(G,'d')\fR
returns the polynomial matrix \fVGt=G(1/z)*z^n\fR where n is the maximum
degree of \fVG\fR.
.LP
For continuous-time systems represented in state-space by a \fVsyslin\fR list,
\fVGt = gtild(G,'c')\fR returns a state-space representation
of \fVG(-s)'\fR i.e the \fVABCD\fR matrices of \fVGt\fR are
\fVA',-C', B', D'\fR. If \fVG\fR is improper (\fV D= D(s)\fR)
the \fVD\fR matrix of \fVGt\fR is \fVD(-s)'\fR.
.LP
For discrete-time systems represented in state-space by a \fVsyslin\fR list,
\fVGt = gtild(G,'d')\fR returns a state-space representation
of \fVG(-1/z)'\fR i.e the (possibly improper) state-space
representation of \fV-z*C*inv(z*A-B)*C + D(1/z) \fR.
.LP
For rational matrices, \fVGt = gtild(G,'c')\fR returns the rational
matrix \fVGt(s)=G(-s)\fR and \fVGt = gtild(G,'d')\fR returns the
rational matrix \fVGt(z)= G(1/z)'\fR.
.LP
The parameter \fVflag\fR is necessary when \fVgtild\fR is called with
a polynomial argument.
.SH EXAMPLE
.nf
//Continuous time
s=poly(0,'s');G=[s,s^3;2+s^3,s^2-5]
Gt=gtild(G,'c')
Gt-horner(G,-s)' //continuous-time interpretation
Gt=gtild(G,'d');
Gt-horner(G,1/s)'*s^3 //discrete-time interpretation
G=ssrand(2,2,3);Gt=gtild(G); //State-space (G is cont. time by default)
clean((horner(ss2tf(G),-s))'-ss2tf(Gt)) //Check
// Discrete-time
z=poly(0,'z');
Gss=ssrand(2,2,3);Gss('dt')='d'; //discrete-time
Gss(5)=[1,2;0,1]; //With a constant D matrix
G=ss2tf(Gss);Gt1=horner(G,1/z)';
Gt=gtild(Gss);
Gt2=clean(ss2tf(Gt)); clean(Gt1-Gt2) //Check
//Improper systems
z=poly(0,'z');
Gss=ssrand(2,2,3);Gss(7)='d'; //discrete-time
Gss(5)=[z,z^2;1+z,3]; //D(z) is polynomial
G=ss2tf(Gss);Gt1=horner(G,1/z)'; //Calculation in transfer form
Gt=gtild(Gss); //..in state-space
Gt2=clean(ss2tf(Gt));clean(Gt1-Gt2) //Check
.fi
.SH SEE ALSO
syslin, horner, factors
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