linearization
sl = lin(sim,x0,u0) [A,B,C,D] = lin(sim, x0, u0)
function
vectors of compatible dimensions
real matrices
syslin
list
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.
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); | ![]() | ![]() |