lin - linearization
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)
deff('[y,xdot]=sim(x,u)','xdot=[u*sin(x);-u*x^2];y=xdot(1)+xdot(2)')
sl=lin(sim,1,2);