Observability
Numerical aspects of linear control

The notion of observability will determine whether knowledge of the output y is sufficient to uniquely determine the state x.

If only certain states (i.e. certain components of the vector x) can be uniquely determined from u and y, these states are said to be observable. A system is therefore completely observable if all its states are observable. Observability means that the initial condition x(t₀) can be calculated from knowledge of the input u (t) and output y (t) over a finite time interval [t₀, t_f ].

We have the fundamental result given by...