On coprime factorizations for parallel interconnections of systems

Abstract

This note is an extension of previous work that gave conditions under which the series or parallel interconnection of two linear, time-invariant systems is completely controllable and observable. Our contribution here presents explicit formulas for the coprime factors of the parallel interconnection in terms of the coprime factors for the constituent subsystems. The resulting characterization has applications to the study of reliability in control systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>