The role of zeros in the performance of multiinput, multioutput feedback systems

A review of the early history attached to the idea of zeros for systems with multiple inputs and outputs is provided. A discussion of the consensus definitions for such zeros is given together with the ways in which they are involved in control thinking and control applications. A control zero principle and a control pole principle explain the intuitive way in which zeros and poles influence the performance of feedback systems. These are presented in the multivariable case by means of a pair of new results, this provides a framework to unify the overall presentation. Zeros at infinity are introduced; the causality of controllers is fitted onto place; and developments in time-varying zeros, nonlinear zeros, and generic zeroes are described