Geodesic
Local assignability of Lyapunov exponents of linear discrete-time system
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 57 (2021), pp. 3-76

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider sufficient and necessary conditions for the proportional local assignability of the Lyapunov spectrum of the system $$ x(m+1)=\left(A(m)+B(m)U(m)\right)x(m), \quad m\in\mathbb Z,\quad x\in\mathbb R^n. $$ The properties of stability of the Lyapunov spectrum and integral separation of linear discrete-time systems are studied, description of the spectral set of a linear system in the case of the full spectrum stability is obtained, the property of uniform complete controllability of a linear system with discrete time is studied, and the properties of the Bebutov shell of a linear discrete-time control system are investigated.
Keywords: linear discrete-time system, Lyapunov exponents, controllability, stabilizability, dynamic shift system. 
@article{IIMI_2021_57_a0,
     author = {I. N. Banshchikova},
     title = {Local assignability of {Lyapunov} exponents of linear discrete-time system},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {3--76},
     publisher = {mathdoc},
     volume = {57},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2021_57_a0/}
}
TY  - JOUR
AU  - I. N. Banshchikova
TI  - Local assignability of Lyapunov exponents of linear discrete-time system
JO  - Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
PY  - 2021
SP  - 3
EP  - 76
VL  - 57
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IIMI_2021_57_a0/
LA  - ru
ID  - IIMI_2021_57_a0
ER  - 
%0 Journal Article
%A I. N. Banshchikova
%T Local assignability of Lyapunov exponents of linear discrete-time system
%J Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
%D 2021
%P 3-76
%V 57
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IIMI_2021_57_a0/
%G ru
%F IIMI_2021_57_a0
I. N. Banshchikova. Local assignability of Lyapunov exponents of linear discrete-time system. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 57 (2021), pp. 3-76. http://geodesic.mathdoc.fr/item/IIMI_2021_57_a0/