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Unformatted text preview: nd asymptotic stability
condition are different.
For linear time-invariant (LTI) systems (to which
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
systems, we use simply “stable” to mean both
BIBO and asymptotic stability. Impulse Response
3 Amplitude 2
-4 0 2 4 6
Time (sec) 8 10 12 6
-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) has at least one simple pole on
G(s) has no multiple poles on
G(s) Does marginal stability imply BIBO stability?
Marginally stable NOT marginally stable TF:
TF: Unstable if a system is neither stable nor
marginally stable. Pick
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
Re(si)<0 for all i.
marginally stable if
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This document was uploaded on 03/02/2014 for the course ME 451 at Michigan State University.
- Spring '08