Strong stabilizability of systems with multiaffine uncertainties and numerator denominator coupling

Abstract

This paper considers a set of proper transfer functions whose numerator and denominator polynomial coefficients display dependent multiaffine parametric uncertainties. It is shown that provided no member transfer function has positive real pole-zero cancellations, all members satisfy the parity interlacing property iff all corner members do the same. Notice that while this implies that each member is strongly stabilizable, it does not imply the existence of a single stable controller that stabilizes the whole set. The paper also shows that whenever the numerator and denominator polynomials lie in dependent polytopes, the task of verifying the absence of positive real pole-zero cancellations can be accomplished by checking the edges.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>