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Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition
book

Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition

by Harold Klee, Randal Allen
April 2016
Intermediate to advanced content levelIntermediate to advanced
815 pages
31h 29m
English
CRC Press
Content preview from Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition
Consider a system with a pair of complex poles of H(z) on the Unit Circle at e
ju
. Its response to
the bounded input u
k
¼sin ku, k ¼0, 1, 2,3,...is obtained from
Y(z) ¼ H(z)U(z) ¼
N(z)
(z e
ju
)(z e
ju
)
sin u z
z
2
(2 cos u)z þ 1
(4:631)
¼
N(z)
(z e
ju
)(z e
ju
)
sin u z
(z e
ju
)(z e
ju
)
(4:632)
¼
sin u zN(z)
(z e
ju
)
2
(z e
ju
)
2
(4:633)
It is left as an exercise to show that y
k
contains a linear combination of the terms, cos ku,
sin ku, k cos ku, and k sin ku. Consequently, the response is unbounded, and the system is not
BIBO stable.
When a real pole of H(z) is located on the Unit Circle at z ¼1orz ¼þ1, and the input is
u
k
¼(1)
k
, k ¼0, 1, 2, 3,
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Publisher Resources

ISBN: 9781439836736