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HW9 - MEEN 651 Control System Design Homework 9...

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MEEN 651 Control System Design Homework 9: Controllability/Observability Assigned: Tuesday, 28 Oct. 2008 Due: Tuesday, 4 Nov. 2008, 5:00 pm Do the following problem from “ Feedback Control of Dynamic Systems ” 5 th ed., Franklin and Powell. Problem 1) Problem 7.5 Problem 2) Problem 7.6 Problem 3) Problem 7.14 (by hand, do not use Matlab) Problem 4) Problem 7.26 Do the following problems: Problem 5) We use the notation A > 0 to denote a positive definite matrix (i.e. symmetric matrix with all positive eigenvalues), and A 0 to denote a positive semi-definite matrix (i.e. symmetric with all eigenvalues greater than or equal to zero). Let A and B be two n x n real matrices which are positive definite. Show that A B if and only if B -1 A -1 . Problem 6) Is the system below controllable? Observable? ( ) ( ) ( ) ( ) [ ] ( ) t x t y t u t x t x 1 0 1 0 0 0 1 1 0 1 2 0 1 0 0 0 1 0 = +
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