Stability analysis of the characteristic polynomials whose coefficients are polynomials of interval parameters via monotonicity methods

We present the conditions of "regional stability" of the characteristic polynomial whose coefficients are polynomials of interval parameters. The regional stability means that all roots of the characteristic polynomial lie in a desired root region in the left-half plane. We construct the desired root region with only one circle whose center is not the origin and radius is not 1. Applying Hermite-Biehler's theorem and transformation to the boundary circle, we derive necessary and sufficient conditions for the regional stability. In order to reduce the amount of calculations for regional stability conditions, we introduce the notion of monotonicity with respect to interval parameters. Our conditions are modified by means of Sturm's chains and the notion of monotonicity. The modified conditions are necessary and sufficient, and use only the endpoint values under the monotonicity assumptions.