Causality and network graph in general bilinear state-space representations

Monika Jozsa (1) , Mihaly Petreczky (2) , M. Kanat Camlibel (3)

1 Mines Douai EMD - École des Mines de Douai
2 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
3 University of Groningen - Department of Mathematics

This paper proposes an extension of the well-known concept of Granger causality, called GB-Granger causality. GB-Granger causality is designed to relate the internal structure of bilinear state-space systems and statistical properties of their output processes. That is, if such a system generates two processes, where one does not GB-Granger cause the other, then it can be interpreted as the interconnection of two subsystems: one that sends information to the other, which does not send information back. This result is an extension of earlier obtained results [1] on the relationship between Granger-causality and the internal structure of linear time-invariant state-space representations.

Domaines: Automatique / Robotique; Optimisation et contrôle [math.OC]

Monika Jozsa, Mihaly Petreczky, M. Kanat Camlibel. Causality and network graph in general bilinear state-space representations. IEEE Transactions on Automatic Control, 2020, 65 (8), pp.3623 - 3630. ⟨10.1109/TAC.2019.2952033⟩. ⟨hal-02398542⟩