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Article Dans Une Revue International Journal of Control, special issue in Honor of Michel Fliess 60 th-birthday Année : 2008

On the convergence of Volterra series of finite dimensional quadratic MIMO systems

Thomas Hélie
Béatrice Laroche

Résumé

In this paper, the Volterra series decomposition of a class of quadratic, time invariant single-input finite dimensional systems is analyzed. The kernels are given by a recursive sequence of linear PDEs in the time domain, and an equivalent algebraic recursion in the Laplace domain. This is used to prove the convergence of the Volterra series to a (possibly weak) trajectory of the system, to provide a practicable value for the radius of convergence of the input in L^oo(R+) and to compute a guaranteed error bound in L^oo(R+) for the truncated series. The result is then extended to MIMO systems. A numerical simulation is performed on an academic SISO example, to illustrate how easily the truncated Volterra series can be implemented.

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Dates et versions

hal-01106316 , version 1 (20-01-2015)

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  • HAL Id : hal-01106316 , version 1

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Thomas Hélie, Béatrice Laroche. On the convergence of Volterra series of finite dimensional quadratic MIMO systems. International Journal of Control, special issue in Honor of Michel Fliess 60 th-birthday, 2008, 81 (3), pp.358-370. ⟨hal-01106316⟩
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