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See the recommended documentation of this function

# routh_t

Routh's table

### Calling Sequence

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

### Arguments

p

a real polynomial

h

a real SISO transfer system

k

a real polynomial or a scalar

r

a matrix

### Description

`r=routh_t(p)` computes Routh's table of the polynomial `h`.

`r=routh_t(h,k)` computes Routh's table of denominator of the system described by transfer matrix SISO `h` with the feedback by the gain `k`.

If `k=poly(0,'k')` we will have a polynomial matrix with dummy variable `k`, formal expression of the Routh table.

### Examples

```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)```

• roots — racines d'un polynôme
• kpure — continuous SISO system limit feedback gain

### Bibliography

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