Diffusive realizations for solutions of some operator equations: The one-dimensional case

Lenczner, Michel; Montseny, Gérard; Yakoubi, Youssef

doi:10.1090/S0025-5718-2011-02485-3

Diffusive realizations for solutions of some operator equations: The one-dimensional case
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by Michel Lenczner, Gérard Montseny and Youssef Yakoubi PDF

Math. Comp. 81 (2012), 319-344 Request permission

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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