Observability

Observability is the property of a system that permits its internal state to be reconstructed from measurements of its outputs. A system is observable if two different initial states necessarily produce different output trajectories; if two states can produce identical outputs forever, the system is unobservable, and those states are indistinguishable from the outside.

The concept originates in control theory and was formalized by Rudolf Kalman for linear systems. Observability is dual to controllability: a system is controllable if its state can be driven anywhere by inputs, and observable if its state can be determined anywhere from outputs. In practice, most systems of interest are only partially observable — the true state must be inferred from noisy, incomplete measurements, a problem that connects observability to state estimation and Bayesian inference.

The observability of a system is not merely a technical property but an epistemic one. It determines what can be known about the system from the outside, and therefore what models of the system are empirically distinguishable.