1987 Volume 23 Issue 4 Pages 379-385
This paper is concerned with the integrity conditions for linear multivariable feedback systems. Integrity is defined as the property such that the closed-loop system remains stable against an arbitrary feedback-loop failure. A new class of matrices, called U-matrix, is introduced, by investigating the properties of the matrices whose all principal minors are units in the set of proper stable rational functions. Based on U-matrix, a necessary and sufficient condition for integrity is given with a stable plant. The result shows that integrity is ensured if and only if the sensitivity matrix is U-matrix as well as the controller being stable. Moreover, using the properties of U-matrix, some sufficient conditions for integrity are derived. It is shown that, if the sensitivity matrix is either strictly positive real or generalized diagonal dominant with all diagonal elements in the set of the units, then integrity is established provided the closed-loop system, as well as the controller, is stable. In terms of the return difference matrix and the closed-loop transfer function matrix, similar results are also derived.
