<ul><li>Deep Selective State-Space Models (SSMs) with discontinuous gating signals pose challenges for stability analysis.</li><li>The stability and regularity properties of continuous-time selective SSMs are investigated using passivity and Input-to-State Stability (ISS).</li><li>Intrinsic energy dissipation in selective SSMs ensures exponential forgetting of past states.</li><li>The research establishes conditions for global ISS, linking local dissipativity to overall system robustness for deep selective SSMs.</li></ul>

Regularity and Stability Properties of Selective SSMs with Discontinuous Gating

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