| Résumé |
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. |
