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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])
r=routh_t(h [,k] [,normalized])

### Arguments

p

a real polynomial

h

a real SISO transfer system

k

a real polynomial or a scalar

normalized

a boolean (%t (default value) or %f)

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 or a rational matrix with dummy variable k, formal expression of the Routh table.

If normalized=%f we will have a polynomial matrix with non normalized elements. In the other case, we will have a rational and normalized matrix.

### Examples

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

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

// Transfer function with formal feedback, non normalized case
routh_t((1+s)/P,poly(0,'k'),%f)

// 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 — roots of polynomials
• 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

### History

 Version Description 5.4.0 A new parameter added: normalized (SEP 89).
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