Eigenvalues and stability - question.

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Hi,

Homework Statement


How may I determine whether a system is stable if its input is equal to its output, hence yielding a system(transfer) function equal to 1?
Furthermore, could an eigenvalue zero characterize a stable system?
I am attaching three examples where I am asked to determine whether the systems are stable or not.


Homework Equations





The Attempt at a Solution


In the first two cases the system's function (transfer function) is 1, hence I am not sure how to determine stability. It seems, though, that the unit is somewhat stable whereas the exponential isn't. As for the bottom sample, do I have to perform a Laplace transform and find H(s) to determine the eigenvalues?
 

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