Does a sampled-data loop tuned on a fixed-period twin survive random sampling intervals?
research/free-jittertwin
Does a sampled-data loop tuned on a fixed-period twin survive random sampling intervals? Uniform jitter up to ±100% never destabilises it, but missed samples do: almost-surely stable up to miss probability 0.556, mean-square stable only to 0.270 (0.05 for a deadbeat tuning); at 0.4 all 2000 simulated runs converge. Stylised scalar model.
What it found
Unstable scalar plant x′ = 3x, gain tuned so the fixed-period twin contracts by 0.5 per sample. Uniform jitter up to ±100% of the period never destabilises it (exact quadrature), but missed samples do: with a sample missed (period doubled) with probability q, the loop is almost-surely stable up to q = 0.556 yet mean-square stable only up to 0.270. Between the two, the mean-square twin metric says “unstable” while 2000 simulated runs at q = 0.4 all converge; past 0.556 they blow up (70% at 0.6). A deadbeat-tuned loop (contraction 0) is fragile: mean-square limit 0.05. Stylised scalar model.
Paper, code and results
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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.