Einstein Product-Based Dynamical Systems

The Einstein product-based dynamical system (EPDS) representation was initially proposed by Chen et al. [Proc. Conf. Control Appl.] in 2019, which utilizes an even-order tensor equipped with the Einstein product to drive the system evolution. This representation is an extension of the TPDS representation and has a form similar to the standard LDS model. EPDSs are well-suited for exploring system-theoretic properties, including stability, reachability, and observability, as well as for developing methods for model reduction and system identification. More importantly, tensor decomposition techniques, such as HOSVD, CPD, and TTD, can be exploited on the even-order dynamic tensors in order to facilitate computation and memory efficiency for EPDSs.