Extreme stability margins of interval systems

The paper deals with the problem of calculating exact extreme stability margins of interval systems consisting of interval plants and fixed controllers based on Bode envelopes. Algorithms are first presented to find the exact extreme phases of an interval real-rational function at a given frequency under the constraint that its module is equal to a given constant. These algorithms are computationally tractable since we need only to calculate phases for six or fewer cases. Then the results on the extreme phases of an interval real-rational function are applied to calculate the extreme case phase and gain margins of an interval system based on its Bode envelope, and to give a new method to find the Nyquist envelope of an interval system