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lin Scilab Group Scilab Function lin
NAME
lin - linearization
CALLING SEQUENCE
[A,B,C,D]=lin(sim,x0,u0)
[sl]=lin(sim,x0,u0)
PARAMETERS
sim : function
x0, u0 : vectors of compatible dimensions
A,B,C,D : real matrices
sl : syslin list
DESCRIPTION
linearization of the non-linear system [y,xdot]=sim(x,u) around x0,u0.
sim is a function which computes y and xdot.
The output is a linear system (syslin list) sl or the four matrices
(A,B,C,D) For example, if ftz is the function passed to ode e.g.
[zd]=ftz(t,z,u)
and if we assume that y=x
[z]=ode(x0,t0,tf,list(ftz,u) compute x(tf).
If simula is the following function:
deff('[y,xd]=simula(x,u)','xd=ftz(tf,x,u); y=x;');
the tangent linear system sl can be obtained by:
[A,B,C,D]=lin(simula,z,u)
sl = syslin('c',A,B,C,D,x0)
EXAMPLE
deff('[y,xdot]=sim(x,u)','xdot=[u*sin(x);-u*x^2];y=xdot(1)+xdot(2)')
sl=lin(sim,1,2);
SEE ALSO
external, derivat
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