quiz4sol - George W. Woodruff School of Mechanical...

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1 George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology ME6403 Digital Control Systems Quiz #4 April 20 2010 (Atlanta main campus), April 27 (DL) NAME (PRINT) Problem 1 (10 points): Find a pair of x 1 and x 2 that minimizes 2 1 2 1 2 2 2 1 2 1 2 2 4 ) , ( x x x x x x x x f . Confirm that the function is minimized by the obtained x 1 and x 2. Solution  0 , 1 2 , 4 1 1 1 1 2 4 1 1 1 2 2 4 ) ( 2 1 2 1 2 1 2 1 2 1 2 2 2 1  c b Q x x x x x x x x x x x x x f 0 8 2 2 2 2 166 . 0 166 . 1 1 2 4 1 1 1 2 1 2 1 1 1  Q b Q x H Problem 2 (10 points): Give an example of a symmetric, 3x3 positive semi-definite matrix in the form
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quiz4sol - George W. Woodruff School of Mechanical...

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