Frequency domain conditions for the stability of perturbed polynomials

New necessary and sufficient conditions for the stability of perturbed polynomials of continuous systems are given in the frequency domain. The conditions are equivalent and in some respects more powerful than the well-known Kharitonov conditions. The new conditions allow considerable freedom in distributing the available uncertainty margin among the different coefficients of a polynomial and provide an indication as to whether the maximum allowable margin of uncertainty for a given polynomial has been reached.     

On the stability of low-order perturbed polynomials

It is shown that for low-order perturbed continuous system polynomials (N⩽6), stability can be guaranteed by checking very simple conditions based on the Hermite-Biehler theorem. For N ⩽5 no numerical computation of the roots is required to check stability. For N=6, one root of a third-order polynomial needs to be found, with the rest of the conditions reducing to simple algorithmic relationships. The result is illustrated by numerical examples     

On common factors appearing in inversion of matrix transfer functions

Two identities that appear when inverting a transfer function matrix T(s)=C(SI-A)?1B are proven. They lead to significant simplification in the computation of T?1(s)