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  "body": "\n## Summary\n\nA [[control system|ZPDTVZQN5K]] with an output is observable if the initial state can be recovered from the known input and the measured output over time.\nObservability matters because in practice only some quantities can be measured, while a feedback law usually needs the full state.\nFor linear systems it is dual to [[controllability|A9WFM77Z4P]]: the pair $(A, C)$ is observable exactly when $(A^T, C^T)$ is controllable.\n\n## Explanations\n\n### L1 human\n\nSuppose you can only see the position of a moving car, not its speed.\nBy watching the position for a while, you can still find the speed, since the speed is the rate of change of the position.\nSo this system is observable even though one quantity is hidden.\nIf you could only see the speed, you would never know where the car started, and the system would not be observable.\n",
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