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

.. _kpure: kpure.html
.. _http://controls.engin.umich.edu/wiki/index.php/RouthStability: http://controls.engin.umich.edu/wiki/index.php/RouthStability
.. _http://www.jdotec.net/s3i/TD_Info/Routh/Routh.pdf: http://www.jdotec.net/s3i/TD_Info/Routh/Routh.pdf
.. _roots: roots.html