Diffusive Realizations for Solutions of Some Operator Equations : the One-Dimensional

Abstract : In this paper we deal with the derivation of state-realizations of linear operators that are solutions to certain operator linear differential equations in one-dimensional bounded domains. We develop two approaches in the framework of diffusive representations: one with complex diffusive symbols; the other with real diffusive symbols. Then, we illustrate the theories and develop numerical methods for a Lyapunov equation arising from optimal control theory of the heat equation. A practical purpose of this approach is real-time computation on a semi-decentralized architecture with low granularity.
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Journal articles
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https://hal.archives-ouvertes.fr/hal-00676355
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Submitted on : Monday, March 5, 2012 - 10:59:47 AM
Last modification on : Friday, October 11, 2019 - 8:22:07 PM

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M. Lenczner, Gérard Montseny, Y. Yakoubi. Diffusive Realizations for Solutions of Some Operator Equations : the One-Dimensional. Mathematics of Computation, American Mathematical Society, 2012, 81, pp.319-344. ⟨10.1090/S0025-5718-2011-02485-3⟩. ⟨hal-00676355⟩

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