Inverse Problems for Matrix Exponential in System Identification: System Aliasing

English

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) > >]

2016

22nd International Symposium on Mathematical Theory of Networks and Systems

Yes

Minneapolis

USA

22nd International Symposium on Mathematical Theory of Networks and Systems

July 12-15

[en] System identification ; matrix inverse ; slow sampled

[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.