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Signals and Systems by Smarajit Ghosh

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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.

 

x2 is unobservable

 

Fig. 9.13 x2 is unobservable

 

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

 

image

 

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 t1tt0, the matrices A

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