Hayden, D and Yuan, Y and Goncalves, J (2014) *Network reconstruction from intrinsic noise: Non-minimum-phase systems.* In: UNSPECIFIED pp. 2329-2334..

## Abstract

This paper considers the problem of inferring the structure and dynamics of an unknown network driven by unknown noise inputs. Equivalently we seek to identify direct causal dependencies among manifest variables only from observations of these variables. We consider linear, time-invariant systems of minimal order and with one noise source per manifest state. It is known that if the transfer matrix from the inputs to manifest states is minimum phase, then this problem has a unique solution, irrespective of the network topology. Here we consider the general case where the transfer matrix may be non-minimum phase and show that solutions are characterized by an Algebraic Riccati Equation (ARE). Each solution to the ARE corresponds to at most one spectral factor of the output spectral density that satisfies the assumptions made. Hence in general the problem may not have a unique solution, but all solutions can be computed by solving an ARE and their number may be finite.

Item Type: | Conference or Workshop Item (UNSPECIFIED) |
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Subjects: | UNSPECIFIED |

Divisions: | Div F > Control |

Depositing User: | Unnamed user with email sms67@cam.ac.uk |

Date Deposited: | 17 Jul 2017 19:45 |

Last Modified: | 09 Sep 2021 03:02 |

DOI: | 10.3182/20140824-6-za-1003.01757 |