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Given a system which is either non-linear and/or time variant, Is there any systematic way to determine if this system is invertible? For example how to determine invertibility of this system? $$\int_{-\infty}^\infty x(5\tau)d\tau$$

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  • $\begingroup$ What is your reasoning behind your assumptions? Like non-linearity or time-variance? $\endgroup$ – Laurent Duval Mar 5 '17 at 16:33
  • $\begingroup$ I mean, if the system is linear and time invariant we could determine its invertibility by convolution. Just check if we could find the impulse response of the system h(t) and find another function g(t) such that their convolution yields impulse function. Does this procedure apply for non-linear or time variant systems also? $\endgroup$ – Sara Mar 5 '17 at 16:43
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In general there is no systematic way and you simply have to analyze the given system. In the case of the system in your question, it's easy to see that it can't be invertible, because the output is just a constant, namely the integral over the input function (assuming this integral exists). There are infinitely many functions which will result in the same value when integrated from $-\infty$ to $\infty$.

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