ps 6 604

# ps 6 604 - Let G s = n G s d G s = s 2 s 1 s 5 s 4 s 3 s 2...

This preview shows pages 1–2. Sign up to view the full content.

ECE 604 LINEAR SYSTEMS Problem Set #6 Issued: Thursday, November 12, 2009 Due: Thursday, November 19, 2009 Problem 1: Consider the p -output homogeneous system ! x t ( ) = Ax t ( ) x 0 ( ) = x 0 y t ( ) = Cx t ( ) We would like to determine the initial state from samples of the output y k ! ( ) for k ! 0 . a) Define ! = e A " . Show that we determine the initial state uniquely from y k ( ) if and only if: rank C C ! C ! 2 ! C ! n " 1 # \$ % % % % % % ( ( ( ( ( ( = n i.e., the sampled-data system is observable ( e A , C ( ) is observable). b) Show that e A , C ( ) (O) implies A , C ( ) is (O). c) Show (by a counterexample) that e A , C ( ) may not be (O) if A , C ( ) is (O). Problem 2:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Let G s ( ) = n G s ( ) d G s ( ) = s 2 ! s + 1 s 5 + s 4 + s 3 + s 2 + s + 1 Give the controllable canonical realization of G s ( ) that has dimension 5. What is the dimension of the minimal realization? Problem 3: Rugh, Problem 10.3, p. 178. Problem 4: Rugh, Problem 10.8, p. 179. Problem 5: Consider the transfer function G s ( ) = s + 1 ( ) 2 s ! 1 ( ) s 2 ! 4 ( ) s s ! 1 " # \$ \$ \$ \$ \$ \$ % & ’ ’ ’ ’ ’ ’ Determine a minimal realization for G ( s ) in controllable canonical form....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

ps 6 604 - Let G s = n G s d G s = s 2 s 1 s 5 s 4 s 3 s 2...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online