Positive Minimal Realization of Continuous-Discrete Linear Systems With All-Pole and All-Zero Transfer Function

Abstract

The positive and minimal realization problem for continuous-discrete linear single-input and single-outputs (SISO) systems is formulated. Two special case of the continuous-discrete systems are given. Method based on the state variable diagram for finding a positive and minimal realization of a given proper transfer function is proposed. Sufficient conditions for the existence of a positive minimal realization of a given proper transfer function of all-pole and all-zero systems are established. Two procedures for computation of a positive minimal realization are proposed and illustrated by a numerical examples.

Optimal design and low noise realization of digital differentiator

“…The principal diagonal elements are the power gains from input to the states. Therefore the noise gains after scaling yields [20,21]…”