Description
Inspect a forward-Euler leak-integrator pole.
Control boundaries and stability terms depend on state history, sign conventions and the full system dynamics. A finite scalar factor, one pole or one frequency sample is not sufficient to establish safe closed-loop behavior.
Inspect a forward-Euler leak-integrator pole.
When to use this tool
Use Discrete Integrator Leak Pole when checking a supplied saturation, hysteresis or local stability condition.
How to use the tool and how it works
- Enter leakRate, step. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read pole, asymptoticallyStable. Inspect asymptoticallyStable before interpreting the associated values.
Inspect a forward-Euler leak-integrator pole. Require leakRate >= 0 and step > 0; pole = 1-leakRate*step and asymptoticallyStable uses abs(pole) < 1.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| leakRate | Leak Rate | Required. Finite number; minimum 0. |
| step | Step duration in the same time unit used by rates and time constants. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| pole | Pole | Required. Finite number. |
| asymptoticallyStable | Strict abs(pole)<1 for this single Euler pole; boundaries -1 and 1 fail. | Required. Boolean. |
{
"input": {
"leakRate": 0.2,
"step": 1
},
"output": {
"pole": 0.8,
"asymptoticallyStable": true
}
}Limitations and assumptions
- Equality at ±1 is not asymptotically stable; this is a scalar linear pole check, not a full-system result.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Analyze the complete dynamic system and practical constraints before interpreting a local result as robust or safe operation.
References
Similar or alternative tools
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