Glad to announce that our paper with Phillip Burt (Escola Politécnica of University of São Paulo) titled “Volterra kernels of bilinear systems have tensor train structure” has been accepted by EUSIPCO 2021! It will be presented at the special session on Tensor and Matrix Methods organized by Rémy Boyer, Nicolas Gillis and Xiao Fu.

In this paper, we show that the Volterra kernels of any bilinear system have a natural and exact tensor-train structure that can be exploited to obtain a low-cost discrete-time “Volterra-like” model for predicting its outputs. This is a valuable property since discrete-time Volterra models (essentially polynomial models with memory) are quite easy to implement and can be made stable by construction by simply truncating their memory; on the other hand, the obtained realization gets very costly with the memory (in samples) and the degree. Furthermore, by virtue of the Carleman bilinearization, this idea can be readily extended to systems with more general nonlinear differential equation that is linear in the input and involves only analytic functions (so-called linear-analytic systems, even though this terminology can be a little misleading).

A preprint is available on HaL : https://hal.archives-ouvertes.fr/hal-03233382v1