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How to evaluate stability of a non-causal System?

  1. Oct 12, 2012 #1
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    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
     
  2. jcsd
  3. Oct 14, 2012 #2

    rude man

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    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?
     
  4. Oct 15, 2012 #3
    @rude man,

    I think your approach gives the proper soln. α should -ve and β by your logic should be positive.
     
  5. Oct 15, 2012 #4

    rude man

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    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.
     
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