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.

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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. 
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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/

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