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Stability theory, including global stability (in dynamical systems, where it can notably be used in combination with ds.dynamical-systems)

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Marginal stability of discrete linear time-invariant system

I have a question about marginal stability of a system: \begin{equation} \mathbf{x}[k] = \mathbf{A}\mathbf{x}[k-1] \end{equation} I would adapt the definition of marginal stability from this question … Most of the references I have found talk about asymptotic stability, and state that spectral radius of matrix should be $\rho(\mathbf{A}) < 1$. …