Lecture 36 : Analysis of LTI systems with rational system functions
Theorem 4
We prove summability of
depends on summability of.
Proof by Induction:
Induction on degree of polynomial
Base
case: (k=1)
Induction step:
Assume
is summable for (k-1) case .we proceed to prove it
for k case.
by our assumption is
summable for polynomial of degree (k-1).
THEOREM :
A neccesary
and sufficient conditon for a continuos rational
system to be a Causal and Stable
is that all the poles must lie in the left half
plane, i.e.
Re (s)< 0.
THEOREM :
A neccesary
and sufficient conditon for a discrete rational
system to be a Causal and Stable
is that all the poles must lie inside the unit circle,
i.e.|z|
< 1 .
depends on summability of
.
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