Frequency Domain Necessary and Sufficient Conditions for Robust Stability of Interval Plants

Considered in this paper is the robust stabilization of a special family of single-input single-output, interval plants in which only the denominator polynomial or the plant poles are uncertain. Two frequency domain necessary and sufficient conditions are derived for the robust stability of the closed loop system. The first stability criterion reduces to a question of whether or not a specially constructed polar plot intersects the box [-0.5,0.5] × [-0.5,0.5] in the complex plane and the second reduces to a question of whether or not the polar plot of the nominal loop transfer function intersects a specially constructed frequency dependent domain in the complex plane. Both criteria can be used in synthesizing controllers for the special class of interval plants considered.