The Volterra series contains a number of terms of order 2 and above. Each of the addends is a generalization of the convolution integral of 2 and higher output signals with 2 and higher output signals, respectively. I read several articles and books - they are used to linearize nonlinear elements in control systems. How to use this series to linearize the parallel product of signals growing exponentially? In Mathcad i made a small calculation - but this is not at all what should turn out. The output of such a system should be the square of the input signal + dynamics of the selected link (if two identical links are multiplied together). Apparently, I do not quite understand the meaning of this series. Please help solve the issue.

https://ibb.co/t8kx604 https://ibb.co/6nxqCMh


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  • $\begingroup$ It is quite hard to understand what you are asking. Can you state your question in a more precise way? $\endgroup$ – fedja May 28 at 21:34
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You read my scheme right. Suppose I give a stepped signal to both of these links = 3. At the output I have to get the output signal 9. The convolution integral is obtained correctly, but the dynamics ... it turns out just an exponential with a double degree. Shouldn't something like 1 / (s + 1) ^ 2 be obtained if the Laplace transform is done after convolution?

  • $\begingroup$ It is a non-linear mapping, so the Laplace transform of the output is not a fixed multiple of the Laplace transform(s) of the input(s) in general. Even if you fix one input to make the mapping linear in the other one, it won't be a pure convolution, so the transfer function will make little or no sense. $\endgroup$ – fedja May 31 at 21:48

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