e483h4_07 - Simon Fraser University School of Engineering...

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Unformatted text preview: Simon Fraser University School of Engineering Science ENSC 483 - Modern Control Systems Spring 2007Assignment 4 1. Find the modal matrix and the Jordan Canonical Form of the following matrices: A = - 1- 1 1 1 3 0 1 0 0 2 1 2- 1- 1- 6 0- 2- 1 2 1 3 0 1 0 0 1 0- 1- 1 1 2 4 1 B = - 1- 2 3- 2 3 2 3 2- 4 1- 2 1- 1- 4- 1- 1 5- 7- 1 2- 4 1- 2- 7- 1- 1 1- 1 1 3- 4 1- 3 1- 1- 4- 1 1- 1 1- 1- 1- 1- 1- 1 1- 1 1- 1 4- 5 2- 3 1- 2- 5- 2 Hint: A has all of its eigenvalues located at = 1, whereas eigenvalues of B are all at =- 1. 2. Let z be an arbitrary n dimensional vector such that P [ z Az A n- 1 z ] is nonsingular. Use the Cayley-Hamilton Theorem to show that the solution of the linear equation problem Px = A n z is x = [...
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e483h4_07 - Simon Fraser University School of Engineering...

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