Show that the system in Figure E.8 is linear, time invariant, BIBO unstable and dynamic.
If there is no excitation, but the zero-excitation response is not zero, the response will grow without bound as time increases.
BIBO Unstable
Causality:
The system equation can be rewritten as
So the response at any time t < t
depends on the excitation at times t < t and not on any future values.
Causal
Memory:
The response at any time depends on the excitation at times .
System is dynamic.
Invertibility:
The system equation,
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