The relation between open-loop and closed-loop properties of multivariable feedback systems

Certain rules of thumb relating open- and closed-loop system properties played an important role in classical design. Examples are "large loop gain implies small disturbance response" and "small loop gain implies small noise response." These rules have previously been generalized to multivariable systems only in special cases. The purpose of this paper is to obtain rules of thumb for systems possessing both large and small gain in different directions at the same frequency. The effect of coupling between high and low gain loops is discussed and generalizations of gain crossover frequency are obtained. The results are illustrated with an example.