problem9

problem9 - EE221A Linear System Theory Problem Set 9...

This preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: EE221A Linear System Theory Problem Set 9 Professor C. Tomlin Department of Electrical Engineering and Computer Sciences, UC Berkeley Fall 2010 Issued 11/23; Due 12/2 Problem 1: How does state feedback affect observability? Consider the following system: bracketleftbigg ˙ x 1 ˙ x 2 bracketrightbigg = bracketleftbigg- 2 1 1 bracketrightbiggbracketleftbigg x 1 x 2 bracketrightbigg + bracketleftbigg 1 bracketrightbigg u (1) y = [1 2] bracketleftbigg x 1 x 2 bracketrightbigg (2) and assume that you would like to design a feedback controller of the form u =- Fx + r , where x = [ x 1 x 2 ] T and r is a reference input signal. (a) Show that the system is observable. (b) Show that there exists a state feedback gain matrix F = [ f 1 f 2 ] such that the closed loop system resulting from setting u =- Fx + r is not observable. (c) Now, compute a matrix F of the form F = [1 f 2 ] such that the closed loop system (as in part (b)) is not observable....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online