Mathematically stable systems

Mathematically stable systems are ones where, when disturbed from their initial state, they naturally settle back to equilibrium over time without oscillating wildly or diverging. In technical terms, this means the system’s responses diminish or stay bounded as time progresses, often due to the properties of its mathematical description (like the location of poles in a control system). Stability ensures predictable, controlled behavior, making the system reliable for practical applications. Essentially, a stable system reacts to changes calmly and doesn't spiral out of control.