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Unformatted text preview: nd asymptotic stability
condition are different.
For linear timeinvariant (LTI) systems (to which
For
we can use Laplace transform and we can
obtain a transfer function), the conditions
happen to be the same.
In this course, we are interested in only LTI
In
systems, we use simply “stable” to mean both
BIBO and asymptotic stability. Impulse Response
5
4
3 Amplitude 2
1
0
1
2
3
4 0 2 4 6
Time (sec) 8 10 12 6
4
2
0
2
4
6 13
5 0 14 5 Remarks on stability (cont’d) Examples Marginally stable if
Marginally Repeated poles
Repeated G(s) has no pole in the open RHP (Right Half Plane), &
G(s)
G(s) has at least one simple pole on
axis, &
G(s)
G(s) has no multiple poles on
axis.
G(s) Does marginal stability imply BIBO stability?
Does
Marginally stable NOT marginally stable TF:
TF: Unstable if a system is neither stable nor
Unstable
marginally stable. Pick
Pick
Output
Output
15 16 Feedback Technique Positive Feedback K
K will depends on the distance between the guitar and the amplifier. 17 Stability summary 18 Mechanical examples: revisited Let si be poles of G.
Then, G is … K f(t)
f(t) M (BIBO, asymptotically) stable if
(BIBO,
Re(si)<0 for all i.
marginally stable if
marginally
Re(si)<=0 fo...
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This document was uploaded on 03/02/2014 for the course ME 451 at Michigan State University.
 Spring '08
 KHAN
 Laplace

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