1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
|
.TH lin 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
lin - linearization
.SH CALLING SEQUENCE
.nf
[A,B,C,D]=lin(sim,x0,u0)
[sl]=lin(sim,x0,u0)
.fi
.SH PARAMETERS
.TP 10
sim
: function
.TP
x0, u0
: vectors of compatible dimensions
.TP
A,B,C,D
: real matrices
.TP
sl
: \fVsyslin\fR list
.SH DESCRIPTION
linearization of the non-linear system \fV[y,xdot]=sim(x,u)\fR
around \fVx0,u0\fR.
.LP
\fVsim\fR is a function which computes \fVy\fR and \fVxdot\fR.
.LP
The output is a linear system (\fVsyslin\fR list) \fVsl\fR or the
four matrices \fV(A,B,C,D)\fR
For example, if \fVftz\fR is the function passed to ode e.g.
.nf
[zd]=ftz(t,z,u)
.fi
and if we assume that \fVy=x\fR
.LP
\fV[z]=ode(x0,t0,tf,list(ftz,u)\fR compute \fVx(tf)\fR.
.LP
If \fVsimula\fR is the following function:
.nf
deff('[y,xd]=simula(x,u)','xd=ftz(tf,x,u); y=x;');
.fi
the tangent linear system \fVsl\fR can be obtained by:
.nf
[A,B,C,D]=lin(simula,z,u)
sl = syslin('c',A,B,C,D,x0)
.fi
.SH EXAMPLE
.nf
deff('[y,xdot]=sim(x,u)','xdot=[u*sin(x);-u*x^2];y=xdot(1)+xdot(2)')
sl=lin(sim,1,2);
.fi
.SH SEE ALSO
external, derivat
|
