EE611

HW#23

Due Monday, November 3

1. a) Prove that by our new definition for observability for time-varying systems, the system:

will be observable iff

is non-singular (W₀ is called the Observability Grammanian) ( means complex conjugate transpose).

b) Use your above proof to find an expression for x(t₀) in terms of y and w.

c) For time-invariant systems, why don't we use your above expression to implement an exact observer instead of the "exponential Luenberger" observer we learned about earlier?