Method for computing state transformations of time‐delay systems

This study provides a systematic method for deriving state transformations of a class of time‐delay systems with multiple output. The significance of this study is that such state transformations can be used to transform time‐delay systems into new coordinates where all the time‐delay terms in the system description are associated with the output and input only. Therefore, in the new coordinate system, a Luenberger‐type state observer can be readily designed. Subsequently, of the three possible versions of the original state vector, namely, instantaneous, delayed, and a mixed of instantaneous and delayed, a state observer which estimates one of these versions can be obtained. This new finding allows the authors to design state observers for a wider class of time‐delay systems. Conditions for the existence of such coordinate changes and an effective algorithm for computing them are provided in this study. A numerical example and simulation results are given to illustrate the simplicity and effectiveness of the proposed method.