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Linear Algebra 5

# Linear Algebra 5 - ECE 531 LINEAR SYSTEM THEORY Take-home...

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ECE 531 LINEAR SYSTEM THEORY SPRING 2006 Take-home Examination #2 Due: Thursday, 4 May 2006 at 6:25pm (in class) This is a take-home exam; open book, open notes. Please list on the exam paper all outside sources (books, notes, etc.) which you consulted in working the problems. You are to work independently , but feel free to contact me should you have any questions. 1. Show how to transform the system ˙ x ( t ) = Ax ( t ) + Bu ( t ) y ( t ) = Cx ( t ) to ˙ z ( t ) = Fz ( t ) + Gu ( t ) y ( t ) = Hz ( t ) via z ( t ) = Px ( t ) so that the z -system is in observer form ; that is, so that F and H have the form F = 0 · · · 0 × × × × × × I . . . . . . . . . × × × × 0 · · · 0 × × × × × . . . I . . . . . . × × × . . . × × 0 · · · 0 × × × × . . . . . . I . . . × × × H = 0 · · · 0 1 × 0 · · · 0 1 × × .

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Linear Algebra 5 - ECE 531 LINEAR SYSTEM THEORY Take-home...

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