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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