EE611

Solution to Homework #23

1. a)

Sufficiency:

Necessity:

Assume system is observable but W_o is singular therefore columns of are linearly dependent

By definition of observable, from knowledge of y and w we can find x(t₀):

Let

Note that y is identically zero!!. Therefore we cannot solve for x(t₀)!!

b)

c) Because again our system (observer) would be open-loop! Not robust to inaccuracies in the model, etc.