Inverse Nyquist array: a quantitative theory

Abstract

Rosenbrock's inverse Nyquist array (INA) (1970, 1974) is made robust for uncertain MIMO systems by direct application of SISO quantitative feedback theory (QFT) methodology to each element of the inverse closed loop system. This enables quantitative bounds to be generated for not only the elements of the closed loop transfer function matrix but also for the overall closed loop interaction index; thereby making precise the heuristic notion of 'sufficient' diagonal dominance used in the traditional Nyquist array. This technique will be used to convert the original MIMO problem into a series of exact robust performance problems involving both parametric and unstructured uncertainty. An illustrative example is presented comparing the solution using this new technique and a mu-synthesis solution.