t-Product-Based Dynamical Systems

The concept of t-product-based dynamical systems (t-PDS) representation was first introduced by Hoover et al. [posted on arXiv] in 2021. The system evolution is governed by the t-product between a third-order dynamic tensor and a third-order state tensor. Recent advancements in tensor decomposition and the algebra of circulants facilitate a natural extension of linear systems theory to t-PDSs, encompassing concepts such as explicit solutions, stability, controllability, and observability. Furthermore, the theory of state feedback control can be extended to t-PDSs in a manner analogous to that of LDSs.