Controllability and Observability
Before designing a controller, two properties must hold: the system must be controllable (inputs can steer it to any state) and observable (outputs reveal the current state). If either fails, no controller can fully stabilize the system (Wikipedia).
Definitions
- Controllable — for every initial state and target state, there exists an input sequence that drives the system from one to the other. If a state is not controllable, no signal can reach it.
- Observable — the system’s internal state can be reconstructed from its outputs. If a state is not observable, the controller cannot detect its behavior.
A state that is uncontrollable but stable is called stabilizable. A state that is unobservable but stable is called detectable. These weaker conditions may suffice in practice.
The fundamental constraint
Every “bad” eigenvalue (unstable mode) of a system must be both controllable and observable. If an unstable mode is uncontrollable, no input can suppress it. If it is unobservable, the controller cannot even detect it. Either way, the closed-loop system inherits the instability.
The fix is physical: add actuators (for controllability) or sensors (for observability).
In software systems
Kubernetes controllers are effective because the API server makes the cluster state both controllable (any resource can be created/updated/deleted) and observable (watch streams report every change). A system with unobservable state — say, a process that modifies files without logging — cannot be reconciled by a controller.
In management
The principle maps directly:
- Observability = measurement. You cannot manage what you cannot measure. If team velocity, customer churn, or deployment frequency are unmeasured, no management framework can close the loop on them.
- Controllability = leverage. Knowing that morale is low (observable) is useless if you have no mechanisms to affect it (uncontrollable). The solution parallels engineering: add actuators (new policies, tools, processes).
This reframes the common adage “you can’t manage what you can’t measure” as a theorem with a precise corollary: and even if you can measure it, you can only manage it if you have a lever to change it.