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Computation of convergence bounds for Volterra series of linear analytic single input systems

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Titre

Computation of convergence bounds for Volterra series of linear analytic single input systems
 

Nom(s)

Helie, Thomas (auteur)
 
Laroche, Béatrice (auteur)
 

Publication

2011
 

Description

Sujet(s)

Nonlinear systems   Volterra series   convergence   guaranteed error
 

Résumé

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 (L^infty([0,T]), L^infty(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.
 

Note(s)

Article paru dans : IEEE Transactions on Automatic Control vol. 56 n°9
 

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Date de la notice

2011-09-30 02:00:00
 

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