A cart-pole stays upright for twelve seconds. Can we call it stable? We can say what happened in that run. A mathematical stability statement needs a model, a precise definition and conditions extending beyond that single trace.
First decide which stability question you mean
BIBO stability asks whether every bounded input keeps a selected output bounded under a stated input-output model. Internal asymptotic stability asks whether every relevant internal deviation decays when the input is removed. Tracking accuracy asks something else again: does the output settle near the target? A motor can be stable but miss the target under load.
A simulation lasting 12 seconds samples only one part of all possible time. A perturbation might grow very slowly, or another bounded input might excite a mode that this trial barely touched.
Report an observation honestly
In the Lab, record plant, controller, seed, initial condition, disturbance, run duration, sensor/output of interest and any rail or actuator limit. Pin a comparison and change one condition. Write 'no divergence observed in this 12-second run under these inputs' rather than 'proved stable'.
A failed finite run is useful evidence of a practical limitation. A successful finite run is useful too. Neither replaces an analytic claim over a defined model and input set.
Name the stability definition, model, input set and time horizon. A plot is an experiment; a theorem needs broader assumptions and proof.
CHECK YOUR UNDERSTANDING: A pole remains upright for 12 seconds under one disturbance. What is the strongest justified conclusion?
Only that no divergence was observed over that time for those stated initial conditions and inputs. BIBO or internal stability needs a defined model and broader analysis.