Stability conditions for the sequential design of non-diagonal multivariable feedback controllers

Sufficient conditions to guarantee closed-loop internal stability for sequentially designed multivariable feedback control systems are developed in this paper. The class of MIMO systems considered have transfer function matrices that are square and invertible. The contributions of these stability conditions to the knowledge base of sequential loop design are two-fold. First, unstable Smith-McMillan pole-zero cancellations in the feedback loop are explicitly considered, thus ensuring internal closed-loop stability. Second, the class of systems addressed is expanded to include MIMO systems with non-minimum phase Smith-McMillan zeros. An important feature of the proposed stability conditions is that the elements of the controller matrix which must be non-zero to achieve internal stability are transparently displayed. As a result, only those off-diagonal controllers needed to achieve the pre-specified stability objectives are used, thus reducing implementation complexity. The application of the stability criteria is demonstrated in a design example for an unstable, non-minimum phase (2 × 2) system.