Extreme point results for robust stabilization of interval plants with first-order compensators

It has been shown previously that a first-order compensator robustly stabilizes an internal plant family if and only if it stabilizes all of the extreme plants. These extreme plants are obtained by considering all possible combinations for the extreme values of the numerator and denominator coefficients. In this work, the authors prove a stronger result, namely, that it is necessary and sufficient to stabilize only sixteen of the extreme plants. These sixteen plants are generated using the Kharitonov polynomials associated with the numerator and denominator. Furthermore, when additional information about the compensator is specified (sign of the gain and signs and relative magnitudes of the pole and zero), then, in some cases, it is necessary and sufficient to stabilize eight critical plants, while, in other cases, it is necessary and sufficient to stabilize twelve critical plants