Izv. IMI UdGU, 2021, Volume 57, Pages 3–76
Local assignability of Lyapunov exponents of linear discrete-time system
I. N. Banshchikova
Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034,
We consider sufficient and necessary conditions for the proportional local assignability of the Lyapunov spectrum of the system
x(m+1)=(A(m)+B(m)U(m))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.
linear discrete-time system, Lyapunov exponents, controllability, stabilizability, dynamic shift system.
|Ministry of Science and Higher Education of the Russian Federation
||075-00232-20-01, проект FEWS-2020-0010
|This research was funded by the Ministry of Science and Higher Education of the Russian Federation in the framework of state assignment No. 075-00232-20-01, project FEWS-2020-0010, and was funded by RFBR, project number 20-01-00293.
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MSC: 39A06, 39A22, 39A30, 93B55
I. N. Banshchikova, “Local assignability of Lyapunov exponents of linear discrete-time system”, Izv. IMI UdGU, 57 (2021), 3–76
Citation in format AMSBIB
\paper Local assignability of Lyapunov exponents of linear discrete-time system
\jour Izv. IMI UdGU
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