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.TH syslin 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
syslin - linear system definition
.SH CALLING SEQUENCE
.nf
[sl]=syslin(dom,A,B,C [,D [,x0] ])
[sl]=syslin(dom,N,D)
[sl]=syslin(dom,H)
.fi
.SH PARAMETERS
.TP 10
dom
: character string (\fV'c'\fR, \fV'd'\fR), or \fV[]\fR or a scalar.
.TP 10
A,B,C,D
: matrices of the state-space representation (\fVD\fR optional
with default value zero matrix). For improper systems \fVD\fR is a polynomial
matrix.
.TP 10
x0
: vector (initial state; default value is \fV0\fR)
.TP 10
N, D
: polynomial matrices
.TP
H
: rational matrix or linear state space representation
.TP 10
sl
: tlist ("\fVsyslin\fR" list) representing the linear system
.SH DESCRIPTION
\fVsyslin\fR defines a linear system as a list and checks consistency of data.
.LP
\fVdom\fR specifies the time domain of the system and can have the following values:
.LP
\fVdom='c'\fR for a continuous time system, \fVdom='d'\fR for a discrete time system,
\fVn\fR for a sampled system with sampling period \fVn\fR (in seconds).
.LP
\fVdom=[]\fR if the time domain is undefined
.LP
State-space representation:
.nf
sl=syslin(dom,A,B,C [,D [,x0] ])
.fi
represents the system :
.nf
s x = A*x + B*u
y = C*x + D*u
x(0) = x0
.fi
The output of \fVsyslin\fR is a list of the following form:
\fV
sl=tlist(['lss','A','B','C','D','X0','dt'],A,B,C,D,x0,dom)
\fR
Note that \fVD\fR is allowed to be a polynomial matrix (improper systems).
.LP
Transfer matrix representation:
.nf
sl=syslin(dom,N,D)
sl=syslin(dom,H)
.fi
The output of \fVsyslin\fR is a list of the following form :
\fVsl=tlist(['r','num','den','dt'],N,D,dom)\fR or \fVsl=tlist(['r','num','den','dt'],H(2),H(3),dom)\fR.
.LP
Linear systems defined as \fVsyslin\fR can be manipulated as
usual matrices (concatenation, extraction, transpose, multiplication, etc)
both in state-space or transfer representation.
.LP
Most of state-space control functions receive a \fVsyslin\fR list as input instead
of the four matrices defining the system.
.SH EXAMPLES
.nf
A=[0,1;0,0];B=[1;1];C=[1,1];
S1=syslin('c',A,B,C) //Linear system definition
S1("A") //Display of A-matrix
S1("X0"), S1("dt") // Display of X0 and time domain
s=poly(0,'s');
D=s;
S2=syslin('c',A,B,C,D)
H1=(1+2*s)/s^2, S1bis=syslin('c',H1)
H2=(1+2*s+s^3)/s^2, S2bis=syslin('c',H2)
S1+S2
[S1,S2]
ss2tf(S1)-S1bis
S1bis+S2bis
S1*S2bis
size(S1)
.fi
.SH SEE ALSO
tlist, lsslist, rlist, ssrand, ss2tf, tf2ss, dscr, abcd
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