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Inverse Problems for Matrix Exponential in System Identification: System Aliasing
Yue, Zuogong; Thunberg, Johan; Goncalves, Jorge
2016In 22nd International Symposium on Mathematical Theory of Networks and Systems
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Keywords :
System identification; matrix inverse; slow sampled
Abstract :
[en] This note addresses identification of the A-matrix in continuous time linear dynamical systems on state-space form. If this matrix is partially known or known to have a sparse structure, such knowledge can be used to simplify the identification. We begin by introducing some general conditions for solvability of the inverse problems for matrix exponential. Next, we introduce “system aliasing” as an issue in the identification of slow sampled systems. Such aliasing give rise to nonunique matrix logarithms. As we show, by imposing additional conditions on and prior knowledge about the A-matrix, the issue of system aliasing can, at least partially, be overcome. Under conditions on the sparsity and the norm of the A-matrix, it is identifiable up to a finite equivalence class.
Disciplines :
Mathematics
Author, co-author :
Yue, Zuogong ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > Life Science Research Unit
Thunberg, Johan ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
Goncalves, Jorge ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
External co-authors :
no
Language :
English
Title :
Inverse Problems for Matrix Exponential in System Identification: System Aliasing
Publication date :
2016
Event name :
22nd International Symposium on Mathematical Theory of Networks and Systems
Event date :
July 12-15
Main work title :
22nd International Symposium on Mathematical Theory of Networks and Systems
Peer reviewed :
Peer reviewed
FnR Project :
FNR9247977 - Causal Dynamical Network Reconstruction From Intrinsic Noise, 2014 (01/09/2014-14/03/2018) - Zuogong Yue
Funders :
FNR - Fonds National de la Recherche [LU]
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