Matched pole-zero state-space model and continuous-time properties

The Matched Pole-Zero (MPZ) model is a widely used technique for discretetime approximation of continuous-time controllers. In this article, a new state-space representation for the (MPZ) model is presented. The new formulation can be used for direct discretization of state-space controllers, and can be easily automated on a digital computer. The most important advantage of the proposed representation is that it preserves the dynamic structure of the original continuous-time realization, i.e. the physical meaning of the states and the direction of eigenvectors remain unchanged. In fact, the new method provides, exactly, the same dynamic state equations as the step-invariant model, together with some modications on the static output state equation. Up to now, due to the lack of such eigenstructure-preserving state-space representations, most of the time domain studies on the eects of discrete approximation of analog controllers were mostly performed using the step-invariant model, although that method is seldom used for actual discretization of controllers. The new formulation paves the way for extending those studies to the case of the more widely used MPZ method.