{
  "annotation_id": "0c6d06eb-75fd-45f7-973b-7c265b443fcc",
  "date_created": "2026-02-17T05:53:20.068000Z",
  "date_modified": "2026-02-17T05:53:20.068000Z",
  "file_hash": "a8263654d3cf70eb420cac2b13ba799386751b40bd5b96eed4d3cd7ca9c6ea33",
  "private": false,
  "record": {
    "abstract": "We study null controllability for linear heat-type systems in finite dimensions that incorporate both memory and time-delay effects. A strengthened notion of controllability, referred to as delay and memory-type null controllability, is introduced, which requires the state, the memory functional, and the delayed history to vanish at the terminal time. Using a duality approach, we establish an augmented observability inequality for the adjoint system and show its equivalence to controllability. In the finite-dimensional setting, this leads to sharp necessary and sufficient algebraic rank conditions extending the classical Kalman criterion to systems with memory and delay.",
    "arxiv_id": "2601.09193",
    "authors": [
      "Dev Prakash Jha",
      "Raju K. George"
    ],
    "categories": [
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Delay and Memory-Type Null Controllability for Heat Equations in Finite Dimensions",
    "url": "https://arxiv.org/abs/2601.09193",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "53a9de26-86f8-420c-927f-f6839a033f6c",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}