sysfact system factorization

## Syntax

    [S, Series] = sysfact(Sys, Gain, flag)

## Arguments

Sys

  `syslin` list containing the matrices `[A,B,C,D]`.

Gain

  real matrix

flag

  string `'post'` or `'pre'`

S

  `syslin` list

Series

  `syslin` list

## Description

If `flag` equals `'post'`, `sysfact` returns in `S` the linear system with ABCD matrices `(A+B*Gain, B , Gain, I)`, and `Series`, a minimal realization of the series system `Sys*S`. If `flag` equals `'pre'`, `sysfact` returns the linear system `(A+Gain*C, Gain , C, I)` and `Series`, a minimal realization of the series system `S*Sys`.

## Examples

    //Kalman filter
    Sys=ssrand(3,2,4);Sys('D')=rand(3,2);
    S=sysfact(Sys,lqr(Sys),'post');
    ww=minss(Sys*S);
    ss2tf(gtild(ww)*ww),Sys('D')'*Sys('D')
    //Kernel
    Sys=ssrand(2,3,4);
    [X,d,F,U,k,Z]=abinv(Sys);
    ss2tf(Sys*Z)
    ss2tf(Sys*sysfact(Sys,F,'post')*U)

## See also

- lqr
- lqe