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arXiv · 2607.03849

Stability of input-output maps and their minimal realizations in state-linear, state-affine, LPV, and linear switched systems

Mihály Petreczky·Juan-Pablo Ortega·Florian Rossmannek·Bálint Daróczy
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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.

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Mihály Petreczky, Juan-Pablo Ortega, Florian Rossmannek, Bálint Daróczy. 2026-07-04. Stability of input-output maps and their minimal realizations in state-linear, state-affine, LPV, and linear switched systems. https://arxiv.org/abs/2607.03849

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