lin

lin — linearization

Calling sequence

[A,B,C,D]=lin(sim,x0,u0)  
[sl]=lin(sim,x0,u0)

`sim`	: function
`x0, u0`	: vectors of compatible dimensions
`A,B,C,D`	: real matrices
`sl`	: `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.



[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);