EE611

Homework #27

Due Friday, November 14

(last HW before Exam 2!!)

1.a) Verify that the following system is deadbeat by finding x_k in terms of x₀ for k=1, 2, 3, and 4

b) Find expressions for A_RO, B_RO, and C_RO, from the reduced-order observer derivation we started in class, where

2. Given the discrete-time system from Homework #26: where

a) Determine the observable eigenvalues for the system

b) Is the system detectable?

c) Design a Full-order discrete observer such that all observable eigenvalues are deadbeat.

d) Draw a block diagram using the controller from Homework #26 and your observer.

e) Repeat parts c) and d) using a reduced-order observer.