STABILITY CRITERION ROUTH

STABILITY CRITERION ROUTH

1. Determine if the system is stable, without the need to calculate roots.

   • Necessary condition
     • All the polynomial coefficients must be positive
     • All the powers of the polynomial in decreasing form must be present.
   • Sufficient condition
     • All the elements of the first column of the triangular arrangement of Routh must be positive.
   • Special cases
     • If a coefficient of the first column is 0.
       • It is replaced by E
     • If a row contains only 0
       • It is replaced by the coefficients of the derived from the auxiliary polynomial that comes from the line 0.

2. Relative stability

   • Replace S with ^ S
     • Equivalent to moving the imaginary axis a quantity Co to the left.