Stöðugleiki

Stöðugleiki, or stability, is a broad concept used to describe how a system behaves when it is subjected to disturbances or changing conditions. In general, a system is considered stable if small perturbations do not lead to wild or unbounded responses, and the system tends to remain near a reference state or return to it after a disturbance. The precise meaning of stability depends on the field and the type of model.

In dynamical systems, stability is often discussed in relation to an equilibrium point. Lyapunov stability means that for any small tolerance, there exists a perturbation bound so that trajectories starting close to the equilibrium stay close for all future times. Asymptotic stability adds convergence to the equilibrium as time progresses, while exponential stability provides a specific exponential rate of convergence. These concepts apply to both continuous- and discrete-time systems.

In control theory and signal processing, stability concerns whether a system produces bounded outputs for bounded inputs (BIBO stability) and whether feedback does not cause unbounded behavior. Robust stability considers uncertainties in the model and aims to ensure stable operation under a range of conditions.

In numerical analysis, stability refers to how errors propagate during computation. An algorithm is numerically stable if small input or rounding errors do not cause large deviations in the result; backward stability means the computed output is the exact solution to a nearby input.

Stöðugleiki is foundational across disciplines, shaping analyses of mechanical, electrical, ecological, economic, and climate systems. It informs design, control, and interpretation of how systems withstand and recover from disturbances.