The existence and uniqueness of volterra series for nonlinear systems

@article{Lesiak1977TheEA,
  title={The existence and uniqueness of volterra series for nonlinear systems},
  author={Casimir Lesiak and Arthur Krener},
  journal={1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications},
  year={1977},
  pages={271-274}
}
Given an input-output map described by a nonlinear control system x = f(x, u) and non-linear output y = h(x), we present a simple straightforward means for obtaining a series representation of the output y(t) in terms of the input u(t). When the control enters linearly x = f(x) + ug(x) the method yields the existence of a Volterra series representation. The proof is constructive and explicitly exhibits the kernels. It depends on standard mathematical tools such as the Fundamental Theorem of… CONTINUE READING

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