Open AccessLocal assignability of Lyapunov exponents of linear discrete-time system
Author(s) -
I.N. Banshchikova
Publication year - 2021
Language(s) - English
DOI - 10.35634/2226-3594-2021-57-01
Subject(s) - controllability , mathematics , lyapunov exponent , spectrum (functional analysis) , discrete time and continuous time , linear system , lyapunov function , control theory (sociology) , stability (learning theory) , linear control systems , mathematical analysis , control (management) , nonlinear system , computer science , physics , statistics , quantum mechanics , artificial intelligence , machine learning
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.