Bounded input bounded output Absolutely summable Absolutely integrable Stability Examples yt 2 t Unstable yt x 2 t Stable yt 2 t x0 Unstable yt 2 ID: 415738
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Slide1
Stability
Bounded input bounded output
Absolutely summable
Absolutely integrable
Slide2
Stability
Examples:y(t) = 2t
Unstabley(t) = x2(t) Stabley(t) = 2t x(0) Unstable
y(t) = 2
t
x(t) Unstable
y(t) = (1/2)
t
x(t) Unstable, t
-
1
blows up,
y(t) = (1/2)
t
u(t) is stableSlide3
Causality
Output does not depend on future values of the input:
Examplesy(t) = x(t+1) Not Causaly(t) = x(t) et+1 Causal y[n] = x[n] + x[n+1] Not Causal