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See the recommended documentation of this function

# lin

linearization

### Syntax

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

### Arguments

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)```

### Examples

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