Geodesic
On the property of integral separation of discrete-time systems
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 27 (2017) no. 4, pp. 481-498 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper is devoted to the study of the property of an integral separation of discrete time-varying linear systems. By definition, the system $x(m+1)=A(m)x(m),$ $m\in\mathbb N,$ $x\in\mathbb R^n,$ is called a system with integral separation if it has a basis of solutions $x^1(\cdot),\ldots,x^n(\cdot)$ such that for some $\gamma>0$, $a>1$ and all natural $m>s$, $i\leqslant n-1$ the inequalities $$ \dfrac{\|x^{i+1}(m)\|}{\|x^{i+1}(s)\|}\geqslant\gamma a^{m-s}\dfrac{\|x^{i}(m)\|}{\|x^{i}(s)\|}. $$ are satisfied. The concept of integral separation of systems with continuous time was introduced by B.F. Bylov in 1965. The criteria for the integral separation of systems with discrete time are proved: reducibility to diagonal form with an integrally separated diagonal; stability and nonmultiplicity of Lyapunov exponents. The property of diagonalizability of discrete-time systems is also studied in detail. The evidence takes into account the specifics of these systems.
Keywords: discrete time-varying linear system, Lyapunov exponents, integral separability, diagonalizability. 
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I. N. Banshchikova; S. N. Popova. On the property of integral separation of discrete-time systems. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 27 (2017) no. 4, pp. 481-498. http://geodesic.mathdoc.fr/item/VUU_2017_27_4_a0/

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