I have a system given that is described by $$x_{k+1} = Ax_k$$ with vectors $x$ and a Matrix $A$ and $k \in \mathbb{N}$. I would like to show that the system is stable and tried to proof that $$\lim_{n \rightarrow \infty}A^n = 0.$$ Or equivalent that $\lVert A \rVert < 1$. Is this sufficient to proof that this system is stable? The question is meant in general for discrete system, hence I have no number examples.
2026-03-26 14:18:56.1774534736
Show that discrete System is stable
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