Floquet theorem for linear implicit nonautonomous difference systems

Authors: Phạm Kỳ Anh, Hà Thị Ngọc Yến,

https://doi.org/10.1016/j.jmaa.2005.08.075

Publisher, magazine: ,

Publication year: 2006

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Abstract

The linear difference system \(A_{n}x_{n+1}+B_{n}x_{n}=q_{n} (n\geq 0)\) is considered, where \(A_n, B_n \in \mathbb R^{m\times m}\) and \(q_n \in \mathbb R^m\) are given. It is assumed also that the singular matrices \(A_n\) have the same rank. The concept and properties of index-1 linear implicit difference system are investigated. Then the Floquet theorem on the representation of the fundamental matrix of index-1 periodic LIDS is established and the Lyapunov reduction theorem is proved. Some examples are discussed.

Tags: implicit difference equations; Floquet theorem; Lyapunov reduction theorem; system