controllability and observability

Controllability refers to the ability to steer a system's behavior or output towards a desired state by applying suitable inputs. A system is considered controllable if it is possible to find inputs that can drive the system from any initial state to any desired final state within a finite amount of time. Observability, on the other hand, refers to the extent to which the internal states of a system can be inferred or determined by observing its outputs. A system is considered observable if its internal states can be uniquely distinguished or estimated by observing its outputs over a finite time period. In summary, controllability is about the ability to manipulate a system's behavior, while observability is about the ability to deduce the internal states of a system based on its outputs.

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