Stability Analysis of the Characteristic Polynomials whose Coefficients are Polynomials of Interval Parameters Using Monotonicity

Abstract

In this paper, we analyze the stability of the characteristic polynomials whose coefficients are polynomials of interval parameters via monotonicity methods. Our stability conditions are based on Frazer-Duncan's theorem and all conditions can be checked using only endpoint values of interval parameters. These stability conditions are necessary and sufficient under the monotonicity assumptions.
When the monotonicity conditions do not hold on the whole parameter region, we present an interval division method and a transformation algorithm in order to apply the monotonicity conditions. Then, our stability analysis methods can be applied to all characteristic polynomials whose coefficients are polynomials of interval parameters.