# sol10 - EE 221: Linear Systems HW #10 Solutions Sam Burden...

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EE 221 : Linear Systems HW #10 Solutions — Sam Burden — Dec 9, 2010 1 Note these solutions are overly terse and leave out some details; in your solutions, you should strive for greater clarity and rigor. Exercise 1. (a) The system is controllable with either column of B , hence either input suﬃces on its own. (b) The system is observable with either sensor. The choice of sensor depends on many factors, including but not limited to: cost; level of noise; reliability. Exercise 2. A = 1 1 1 - a 4 - a 3 - a 2 - a 1 ,B = 0 0 0 1 . The system is in control canonical form, whence the closed-loop characteristic polynomial is χ ( s ) = s 4 +( a 1 + f 4 ) s 3 + ( a 2 + f 3 ) s 2 +( a 3 + f 2 ) s +( a 4 + f 1 ). The desired characteristic polynomial is ξ ( s ) = s 4 +4 s 3 + 7 s 2 + 6 s + 2, whence f 1 = 2 - a 4 ,f 2 = 6 - a 3 ,f 3 = 7 - a 2 ,f 4 = 4 - a 1 . Exercise

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## This note was uploaded on 04/11/2011 for the course EE 221A taught by Professor Clairetomlin during the Fall '10 term at Berkeley.

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sol10 - EE 221: Linear Systems HW #10 Solutions Sam Burden...

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