{"ID":5937959,"CreatedAt":"2026-07-07T03:14:33.014478982Z","UpdatedAt":"2026-07-07T12:19:32.242771905Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.03849","arxiv_id":"2607.03849","title":"Stability of input-output maps and their minimal realizations in state-linear, state-affine, LPV, and linear switched systems","abstract":"Stability is often assumed in learning and identification, yet it is rarely characterized directly from input--output data. We show that an input--output family admits a stable finite-dimensional state-linear realization iff it has finite Hankel-rank and its response decays uniformly with time; for state-linear realizable maps this decay is necessarily exponential. We extend these results to state-affine, LPV, and linear switched systems via suitable input-forgetting notions, and relate forgetting to decay of impulse responses (sub-Markov parameters). In all cases, the decay/forgetting rate determines the decay rate of every minimal realization.","short_abstract":"Stability is often assumed in learning and identification, yet it is rarely characterized directly from input--output data. We show that an input--output family admits a stable finite-dimensional state-linear realization iff it has finite Hankel-rank and its response decays uniformly with time; for state-linear realiza...","url_abs":"https://arxiv.org/abs/2607.03849","url_pdf":"https://arxiv.org/pdf/2607.03849v1","authors":"[\"Mihály Petreczky\",\"Juan-Pablo Ortega\",\"Florian Rossmannek\",\"Bálint Daróczy\"]","published":"2026-07-04T12:37:09Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}