A Frequency Domain Criterion for Robustly Stabilizing a Family of Interval Plants

Abstract

Considered in this paper is the problem of robust stabilization of a family of interval plants by a single fixed compensator. A frequency domain sufficient condition determines the closed-loop stability. In particular if a specially constructed frequency function does not, at any frequency ω ∈ [0, ∞], intersect the box [−1, 1] × [−1, 1] in the complex plane then the entire closed loop family is stable. Also identified is a class of interval plants for which the sufficient condition in fact does become necessary.