How to evaluate stability of a non-causal System?

[rudra]

For this problem I have taken laplace(one-sided) transform of h(t) which gives me
H(s)=1/(s-α). From this I can state that α must be -ve for G(s) to be stable.
But my problem is while taking one-sided Laplace Transform the exp(βt)u(-t) part gives 0.
So in H(s) according to my calculation, β doesn't appear. I don't know what I am doing wrong. Please help

 

[rude man]

For this problem I have taken laplace(one-sided) transform of h(t) which gives me
H(s)=1/(s-α). From this I can state that α must be -ve for G(s) to be stable.
But my problem is while taking one-sided Laplace Transform the exp(βt)u(-t) part gives 0.
So in H(s) according to my calculation, β doesn't appear. I don't know what I am doing wrong. Please help

As I said, this problem deals with a nonexistent situation (anyone diosagree?).

But: the u(t) part is easy: what does exp(αt) do as t → ∞?

Now for the noncausal part: u(-t) = 1 for t < 0 and = 0 for t => 0. So for any negative value of t, what does exp(βt) do as t gets more and more negative, approaching t → -∞, with β positive or negative?

 

[rudra]

@rude man,

I think your approach gives the proper soln. α should -ve and β by your logic should be positive.

 

[rude man]

@rude man,

I think your approach gives the proper soln. α should -ve and β by your logic should be positive.

That's where I would put my chips. t → -t in the u(-t) term.

I still think you should ask your prof if that problem has any physical meaning. Unless you're a math purist I see no reason to worry about it.