Matched‐pole–zero discrete‐time model in the state‐space representation

Abstract

In this paper, the matched-pole-zero model which has been widely used for discretisation of a single-input-singleoutput control system described in transfer-function forms is extended to be applicable to the system in state-space forms. The matched-pole-zero model is classified as the discrete-time model, where poles and transmission zeros are mapped into the discrete-time domain according to the same discretisation law defined by a certain algebraic relationship. In order to obtain the matched-pole-zero model, the paper presents an equivalent reconfiguration, which transforms a system into an internal feedback structure around a subsystem based on the principle of control zeros. Discretisation of the subsystem produces a discrete-time model, where transmission zeros are mapped according to the desired law. The proposed matched-pole-zero model is obtained by modifying the pole placements of this discrete-time model. As long as the direct-term matrix of the underlying system is nonsingular, the proposed model can be obtained algorithmically and is applicable to a multi-input-multioutput system without any modification. The paper provides numerical examples verifying that the proposed matched-pole-zero model preserves the unique characteristics of the underlying system due to the zeros, such as the blocking and the decoupling properties, and causes smaller discretisation errors than the comparable matched-pole-zero model.