balreal balanced realization

## Syntax

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

## Arguments

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