Control ENG HW_Part_63

# Control ENG HW_Part_63 - Z= 1+ s 1− s (1 + x ) + iy (1...

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Unformatted text preview: Z= 1+ s 1− s (1 + x ) + iy (1 − x) + iy (1 − x) − iy (1 − x) + iy (1 − x 2 + (1 = x + 1 − x)iy − y 2 ) 1 + x 2 − 2x + y 2 = 1 − ( x 2 + y 2 ) + 2iy 1 − 2x + (x 2 + y 2 ) Re(Z ) = 1 − (x2 + y 2 ) 1 − 2x + (x 2 + y 2 ) if Re( z ) > 0 then 1 − ( x 2 + y 2 ) > 0 and 1 − 2x + (x 2 + y 2 ) > 0 we have x 2 + y 2 <1 x2 + y2 < 1 Ranges are − 1 < x < 1 −1 < y < 1 Po int s in the unit circle 1 − ( x 2 + y 2 ) > 0 is true therefore x 2 + y 2 < 1 Now 1 + (x 2 + y 2 ) − 2x if x = −1& y = 0 then it is 4 if x = 1 & y = 0 then it is 0 0 < (1 + ( x 2 + y 2 ) − 2 x) < 4 Re( z ) > 0 example: if s = (0.5 + i0.5) the system is unstable due to the real part 1 L−1 s − (0.5 + i 0.5) ...
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## This note was uploaded on 11/13/2011 for the course COP 4355 taught by Professor Koslov during the Spring '10 term at University of Florida.

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