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# routh_t

ラウス表

### 呼び出し手順

```r=routh_t(p)
r=routh_t(h [,k])```

p

h

k

r

### 説明

`r=routh_t(p)` は 多項式`h`のラウス表を計算します.

`r=routh_t(h,k)` は, ゲイン`k`によるフィードバックを有する SISO伝達行列 `h`で記述されたシステムの 分母のラウス表を計算します.

`k=poly(0,'k')` の場合,ダミー変数`k` で表した多項式行列でラウス表が記述されます.

### 例

```s=%s;
P=5*s^3-10*s^2+7*s+20;
routh_t(P)

//transfer function with formal feedback
routh_t((1+s)/P,poly(0,'k'))

// One of the coefficients in the polynomial equals zero
P1=2*s^3-24*s+32;
routh_t(P1)

// A row full of zeros
P2=s^4-6*s^3+10*s^2-6*s+9;
routh_t(P2)```

### 参照

• roots — 多項式の根
• kpure — 連続SISOシステムの限界フィードバックゲイン

### 参考文献

http://controls.engin.umich.edu/wiki/index.php/RouthStability

http://www.jdotec.net/s3i/TD_Info/Routh/Routh.pdf

Comments on the Routh-Hurwitz criterion, Shamash, Y.,Automatic Control, IEEE T.A.C Volume 25, Issue 1, Feb 1980 Page(s): 132 - 133

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