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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https://hal-supelec.archives-ouvertes.fr/hal-00655910
Contributor : Béatrice Laroche <>
Submitted on : Tuesday, January 3, 2012 - 10:15:06 AM
Last modification on : Thursday, May 16, 2019 - 1:16:35 AM

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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, Institute of Electrical and Electronics Engineers, 2011, 56 (9), pp.2062-2072. ⟨10.1109/TAC.2010.2091435⟩. ⟨hal-00655910⟩

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