This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: EE221A Linear System Theory Final Exam Professor C. Tomlin Department of Electrical Engineering and Computer Sciences, UC Berkeley Fall 2010 12/14/10, 36pm Your answers must be supported by analysis, proof, or counterexample. There are 9 questions: Please make sure your exam paper has all 9 questions. Approximate points for each question are indicated. The exam is out of 85 points total. You are allowed to use 2 8 . 5 × 11 crib sheets (one side on each). 1 Problem 1: Properties of interconnected subsystems (10 points). Figure 1: Interconnected subsystems, for Problem 1. Consider the interconnected systems ( i ) and ( ii ) shown in Figure 1. For each of these systems, (a) (5 points) Determine the internal stability of the resulting interconnection. (b) (5 points) Is the resulting interconnection controllable? Observable? Explain. 2 Problem 2: Eigenvalue assignment (10 points). Consider the SISO LTI system in controllable canonical form: ˙ x = Ax + Bu,x ( t ) ∈ R n ,u ( t ) ∈ R where A = 1 ··· 1 ··· . . . . . . . . . . . . . . . . . . 1 α 1 α 2 α 3 ···  α n 1 α n , B = . . . 1 (a) (3 points) Determine the characteristic polynomial of the closed loop system for u = Kx , where K = [...
View
Full
Document
This note was uploaded on 12/09/2011 for the course EE 221A taught by Professor Clairetomlin during the Fall '10 term at Berkeley.
 Fall '10
 ClaireTomlin
 Electrical Engineering

Click to edit the document details