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)

See Also

• 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