Signals and Systems

9.10 OBSERVABILITY

If any state of a system can not be observed from measurements, it is called unobservable. From Fig. 9.13, it is clear that the state x₂ is not connected to output. Therefore the state x₂ is called unobservable.

 

 

Fig. 9.13 x₂ is unobservable

 

Any linear time invariant system can be represented by the dynamic equation

 

 

and         y(t) = Cx(t) + Du(t)

 

The state x(t) is said to be observable if there exists a finite time t₁ ≥ 0 for any given input u(t) so that the knowledge of u(t) for t₁ ≥ t ≥ t₀, the matrices A