A system is described by 
. Classify this system as to time invariance, BIBO stability and invertibility.
What will be an ideal response?
Solution:
Time invariant
BIBO Stability:
If the excitation is a constant, the response increases without bound.
BIBO Unstable
Causality:
At any time n = 
the response depends on the excitation at the next time in the future.
Not causal.
Memory:
At any time n = the response depends on the excitation at that time and previous times.
System has memory.
Invertibility:
Inverting the functional relationship, 
Taking the first backward difference of both sides of the original system equation,
The excitation is uniquely determined by the response.
Invertible.
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