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%0 Conference Proceedings
%A Hélie, Thomas
%A Laroche, Béatrice
%T Computation of convergence radius and error bounds of Volterra series for single input systems with a polynomial nonlinearity
%D 2009
%B IEEE Conference on Decision and Control
%C Shanghai
%V 48
%P 1-6
%F Helie09b
%X In this paper, the Volterra series decomposition of a class of time invariant system, polynomial in the state and affine in the input, with an exponentially stable linear part is analyzed. A formal recursive expression of Volterra kernels of the input-to-state system is derived and the singular inversion theorem is used to prove the non-local-in-time convergence of the Volterra series to a trajectory of the system, to provide an easily computable value for the radius of convergence and to compute a guaranteed error bound for the truncated series. These results are available for infinite norms (Bounded Input Bounded Output results) and also for specific weighted norms adapted to some so-called ``fading memory systems'' (exponentially decreasing input-output results). The method is illustrated on two examples including a Duffing's Oscillator.
%1 6
%2 3
%U http://articles.ircam.fr/textes/Helie09b/