Difference flatness of discrete-time linear time-delay systems and transformation to fully actuated systems

This paper investigates the difference flatness of discrete-time linear time-delay systems (TDSs). Initially, by employing matrix augmentation techniques and model reduction methods, the discrete-time linear TDSs can be transformed into the discrete-time linear delay-free systems while preserving controllability equivalence. Subsequently, a coprime factorisation approach for the transfer function matrix of discrete-time linear delay-free systems is utilised to construct the flat output of the discrete-time linear TDSs. Based on this, the discrete-time linear TDSs can be equivalently transformed into the discrete-time fully actuated system (FAS) with the constructed flat output as the generalised state, and the pole assignment problem of discrete-time TDSs can be directly addressed. Numerical examples demonstrates the effectiveness of the proposed approach.