A “relaxation” approach for the hankel approximation of some vibrating structures

Nadia Maïzi (1)

1 CMA - Centre de Mathématiques Appliquées

We present here an approach for the rational approximation of infinite dimensional linear systems with infinitely many poles on the imaginary axis, that is to say neither stable nor unstable. This approach is based on the “relaxation” of the input and output spaces associated with the original system; it maintains the input-output behaviour described by the system. Applying it to some linear systems corresponding to vibrating structures yields results which depend on the rate of growth of the associated poles.

Mots clés: Infinite-dimensional systems; Error-bounds

Domaines: Automatique

Nadia Maïzi. A “relaxation” approach for the hankel approximation of some vibrating structures. R.F. Curtain, editor ; A. Bensoussan, J.L. Lions, honorary eds. Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems. Proceedings of the 10th international conference, Sophia-Antipolis, France, June 9-12, 1992, Springer Verlag, pp.585-597, 1993, Lecture Notes in Control and Information Sciences ; Volume 185, ⟨10.1007/BFb0115017⟩. ⟨hal-00505098⟩