final_f10

final_f10 - EE221A Linear System Theory Final Exam...

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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, 3-6pm 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 = [...
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This note was uploaded on 12/09/2011 for the course EE 221A taught by Professor Clairetomlin during the Fall '10 term at Berkeley.

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final_f10 - EE221A Linear System Theory Final Exam...

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