EE611

HW#19
Due Friday, October 24

1. a) Prove the separation principle (i.e., prove that the eigenvalues of the combined observer/controller closed loop system are the {eigenvalues of A-BK} U {eigenvalues of A-KoC}).

b) Show that a similarity transformation does not affect controllability (i.e., if (A,B) is controllable, then (T^-1AT, T^-1B) is controllable.

c) Show that feedback does not affect controllability (i.e., if (A,B) is controllable, then (A_new, B) is controllable where A_new=A-BK_f).

2. Recall the 5^th-order system from HW#18:

a) Design an improved-observer such that all the observable eigenvalues are {-10}

b) Draw a block diagram of your design combined with your controller from HW#18