balreal

Scilab Function
Last update : April 1993

balreal - balanced realization

### Calling Sequence

  `[slb [,U] ] = balreal(sl)`

### Parameters

- `sl,slb` : linear systems (`syslin` lists)

### Description

Balanced realization of linear system `sl=[A,B,C,D]` . `sl` can be a continuous-time or discrete-time state-space system. sl is assumed stable.

    slb=[inv(U)*A*U ,inv(U)*B , C*U , D]

is the balanced realization.

`slb` is returned as a `syslin` list.

### Examples

    A=diag([-1,-2,-3,-4,-5]);B=rand(5,2);C=rand(1,5);
    sl=syslin('c',A,B,C);
    [slb,U]=balreal(sl);
    Wc=clean(ctr_gram(slb))
    W0=clean(obs_gram(slb))

### See Also

`ctr_gram` , `obs_gram` , `hankelsv` , `equil` , `equil1` ,