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

The matched pole-zero (mpz) model is a widely used technique for discretetimeapproximation of continuous-time controllers. in this article, a new state-spacerepresentation for the (mpz) model is presented. the new formulation can be used fordirect discretization of state-space controllers, and can be easily automated on a digitalcomputer. the most important advantage of the proposed representation is that it preservesthe dynamic structure of the original continuous-time realization, i.e. the physical meaningof the states and the direction of eigenvectors remain unchanged. in fact, the new methodprovides, exactly, the same dynamic state equations as the step-invariant model, togetherwith some modications 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 analogcontrollers were mostly performed using the step-invariant model, although that methodis seldom used for actual discretization of controllers. the new formulation paves the wayfor extending those studies to the case of the more widely used mpz method.