Controllability and observability

State controllability and observability are key properties in linear input–output systems in state-space form. In the state-space approach, the relation between inputs and outputs is represented using the state variables of the system. A natural question is then to what extent it is possible to manipulate the values of the state vector by means of an appropriate choice of the input function. The concepts of controllability, reachability, and null controllability address this issue. Another important question is whether it is possible to uniquely determine the values of the state vector from knowledge of the input and output signals over a given time interval. This question is dealt with using the concept of observability