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Recovering the observable part of the initial data of an infinite-dimensional linear system with skew-adjoint generator

Haine, Ghislain Recovering the observable part of the initial data of an infinite-dimensional linear system with skew-adjoint generator. (2014) Mathematics of Control, Signals, and Systems, 26 (3). 435-462. ISSN 0932-4194

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Official URL: http://dx.doi.org/10.1007/s00498-014-0124-z

Abstract

We consider the problem of recovering the initial data (or initial state) of infinite-dimensional linear systems with unitary semigroups. It is well-known that this inverse problem is well posed if the system is exactly observable, but this assumption may be very restrictive in some applications. In this paper we are interested in systems which are not exactly observable, and in particular, where we cannot expect a full reconstruction. We propose to use the algorithm studied by Ramdani et al. in (Automatica 46:1616–1625, 2010) and prove that it always converges towards the observable part of the initial state. We give necessary and sufficient condition to have an exponential rate of convergence. Numerical simulations are presented to illustratethe theoretical results.

Item Type:Article
Additional Information:Thanks to Springer editor. The definitive version is available at http://www.springerlink.com. The original PDF of the article can be found at Mathematics of Control, Signals, and Systems website: http://link.springer.com/journal/498/content/l81280
HAL Id:hal-00934239
Audience (journal):International peer-reviewed journal
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Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
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Deposited By: Ghislain Haine
Deposited On:21 Jan 2014 15:52

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