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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 multiple input systems with an analytic nonlinearity in state
%D 2010
%B IEEE Conference on Decision and Control
%C Atlanta
%V 49
%P 1-6
%F Helie10j
%X In this paper, the Volterra series decomposition of a class of multiple input time-invariant systems, analytic in state and affine in inputs is addressed. Computable bounds for the non-local-in-time convergence of the Volterra series to a trajectory of the system are given for infinite norms (Bounded Input Bounded Output results) and for specific weighted norms adapted to some ``fading memory systems'' (exponentially decreasing input-output results). This work extends results previously obtained for polynomial single input systems. Besides the increase in combinatorial complexity, a major difference with the single input case is that inputs may play different roles in the system behavior. Two types of inputs (called ``principal'' and ``auxiliary'') are distinguished in the convergence process to improve the accuracy of the bounds. The method is illustrated on the example of a frequency-modulated Duffing's oscillator.
%1 6
%2 3
%U http://articles.ircam.fr/textes/Helie10j/