stabil

Scilab Function
Last update : 25/04/2007

stabil - stabilization

### Calling Sequence

  `F=stabil(A,B,alfa)`
  `K=stabil(Sys,alfa,beta)`

### Parameters

- `A` : square real matrix (`nx x nx` )
- `B` : real matrix (`nx x nu` )
- `alfa, beta` : real or complex vector (in conjugate pairs) or real number.
- `F` : real matrix (`nx x nu` )
- `Sys` : linear system (`syslin` list) (`m` inputs, `p` outputs).
- `K` : linear system (`p` inputs, `m` outputs)

### Description

`F=stabil(A,B,alfa)` returns a gain matrix `F` such that `A+B*F` is stable if pair `(A,B)` is stabilizable. Assignable poles are set to `alfa(1),alfa(2),...` . If `(A,B)` is not stabilizable a warning is given and assignable poles are set to `alfa(1),alfa(2),...` . If `alfa` is a number all eigenvalues are set to this `alfa` (default value is `alfa=-1` ).

`K=stabil(Sys,alfa,beta)` returns `K` , a compensator for `Sys` such that `(A,B)` -controllable eigenvalues are set to `alfa` and `(C,A)` -observable eigenvalues are set to `beta` .

All assignable closed loop poles (which are given by the eigenvalues of `Aclosed=h_cl(Sys,K)` are set to `alfa(i)` 's and `beta(j)` 's.

### Examples

    // Gain:
    Sys=ssrand(0,2,5,list('st',2,3,3));
    A=Sys('A');B=Sys('B');F=stabil(A,B);
    spec(A) //2 controllable modes 2 unstable uncontrollable modes
    //and one stable uncontrollable mode
    spec(A+B*F) //the two controllable modes are set to -1.
    // Compensator:
    Sys=ssrand(3,2,5,list('st',2,3,3)); //3 outputs, 2 inputs, 5 states
    //2 controllables modes, 3 controllable or stabilizable modes.
    K=stabil(Sys,-2,-3);  //Compensator for Sys.
    spec(Sys('A'))
    spec(h_cl(Sys,K))   //K Stabilizes what can be stabilized.

### See Also

`st_ility` , `contr` , `ppol` ,