Novel model of non-uniformly sampled-data systems based on a time-varying backward shift operator

• NUSD systems with asynchronous input–output data have been considered.
• A novel model is proposed by introducing a time-varying backward shift operator.
• The proposed model is much simpler than the lifted models.
• The equivalence between the proposed model and the lifted models has been proved.
• Identification and control design for NUSD systems based on the proposed model have been discussed.

Based on the lifting technique, the lifted state space model and the lifted transfer function model can be derived to describe non-uniformly sampled-data (NUSD) systems. However, the lifted models are inconvenient for both identification and control purposes due to the causality constraint and the model complexity. To solve this problem, a novel model of NUSD systems is proposed by introducing a time-varying backward shift operator. The proposed model is more concise in structure and has fewer parameters than the lifted models, using which the traditional identification methods and control strategies of single-rate systems can be easily extended to NUSD systems. The advantages and effectiveness of the proposed model are well illustrated by a simulation example.