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dcgain

confirmedshipPythonModel behavior & reasoningJuly 22, 2026

the question

Does Mamba's steady-state (DC) gain hold at the continuous value -B/A, or is it distorted by inconsistent input-branch discretization?

what came out

Distorted. The state branch uses ZOH but the input branch uses Euler (Mamba-2) or trapezoidal (Mamba-3), so the DC gain inflates by exactly z/(e^z-1) or (z/2)coth(z/2) with z=Delta*A, unbounded (~|z|) in the reset regime and reached in normal operation (11x, 64x measured). No constant blend lambda restores it; lambda*(z) runs 0.49 to 0.05.

method & receipts

  • Result: confirmed
  • Tested — a correctness/benchmark suite ships alongside the code.

→ read the code and re-run it

github.com/v-code01/dcgain