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Controllability is an important property of a control system, and the controllability property plays a crucial role in many control problems, such as stabilization of unstable systems by feedback, or optimal control.
Controllability and observability are dual aspects of the same problem.
Roughly, the concept of controllability denotes the ability to move a system around in its entire configuration space using only certain admissible manipulations. The exact definition varies slightly within the framework or the type of models applied.
The following are examples of variations of controllability notions which have been introduced in the systems and control literature:
State controllability
Output controllability
Controllability in the behavioural framework

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