feedback

Scilab Function
Last update : April 1993

feedback - feedback operation

### Calling Sequence

  `Sl=Sl1/.Sl2`

### Parameters

- `Sl1,Sl2`: linear systems (`syslin` list) in state-space or transfer form, or ordinary gain matrices.
- `Sl`: linear system (`syslin` list) in state-space or transfer form

### Description

The feedback operation is denoted by `/.` (slashdot). This command returns `Sl=Sl1*(I+Sl2*Sl1)^-1`, i.e the (negative) feedback of `Sl1` and `Sl2`. `Sl` is the transfer `v -> y` for `y = Sl1 u`, `u = v - Sl2 y`.

The result is the same as `Sl=LFT([0,I;I,-Sl2],Sl1)`.

Caution: do not use with decimal point (e.g. `1/.1` is ambiguous!)

### Examples

    S1=ssrand(2,2,3);S2=ssrand(2,2,2);
    W=S1/.S2;
    ss2tf(S1/.S2)
    //Same operation by LFT:
    ss2tf(lft([zeros(2,2),eye(2,2);eye(2,2),-S2],S1))
    //Other approach: with constant feedback
    BigS=sysdiag(S1,S2); F=[zeros(2,2),eye(2,2);-eye(2,2),zeros(2,2)];
    Bigclosed=BigS/.F;
    W1=Bigclosed(1:2,1:2);   //W1=W (in state-space).
    ss2tf(W1)
    //Inverting
    ss2tf(S1*inv(eye()+S2*S1))

### See Also

`lft`, `sysdiag`, `augment`, `obscont`,