Frequency Domain Criteria for Synthesizing Robustly Stabilizing Compensators for a Class of Interval Plants

Abstract

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 [−1, 1] × [−1, 1] 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 for synthesizing controllers for the special class of interval plants considered. A loop shaping technique is proposed for the synthesis of a robustly stabilizing compensator. For the special class of interval plants considered, the polar plot of the nominal loop transfer function must not intersect a frequency dependent parallelogram. The four corners of the parallelogram can be explicitly computed at each frequency.