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Journal Articles IEEE Transactions on Automatic Control Year : 2011

Computation of Convergence Bounds for Volterra Series of Linear-Analytic Single-Input Systems

Abstract

In this paper, the Volterra series decomposition of a class of single-input time-invariant systems, analytic in state and affine in input, is analyzed. Input-to-state convergence results are obtained for several typical norms (Linf[0,T], Linf (R+) as well as exponentially weighted norms). From the standard recursive construction of Volterra kernels, new estimates of the kernel norms are derived. The singular inversion theorem is then used to obtain the main result of the paper, namely, an easily computable bound of the convergence radius. Guaranteed error bounds for the truncated series are also provided. The relevance of the method is illustrated in several examples.
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Dates and versions

hal-00655910 , version 1 (03-01-2012)

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Thomas Hélie, Béatrice Laroche. Computation of Convergence Bounds for Volterra Series of Linear-Analytic Single-Input Systems. IEEE Transactions on Automatic Control, 2011, 56 (9), pp.2062-2072. ⟨10.1109/TAC.2010.2091435⟩. ⟨hal-00655910⟩
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