Explicit Solution to Quasi-Polynomial Matrix Right Coprime Factorization with Application in Establishment of Time-Delay Fully Actuated System

We investigate the right coprime factorization of the transfer function matrix of a linear time-delay system considering constant state and input delays. This transfer function matrix is a quasi-polynomial matrix, and its right coprime factorization can be explicitly obtained by solving a series of linear equations once a user-specified Pseudo-Controllability Indices (PCI) set is selected. Besides, we determine the condition for the PCI set such that the denominator matrix in the right coprime factorization is column reduced. We then utilize these results to transform the original time-delay system into a fully actuated one. Finally, an example demonstrates the effectiveness of our method.