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Multidimensional causality and passivity of linear and nonlinear systems arising from physics

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Abstract

We start with the general notions of causality, passivity, losslessness and related concepts for a class of multidimensional systems, in particular with multidimensional causality and passivity, arising from physical considerations. While such definitions are nowhere restricted to linear systems we show that when applied to linear systems with constant parameters (coefficients) they boil down to standard notions of passivity described by positive real functions and matrices, or equivalently, by bounded real functions and matrices in several complex variables.

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Authors and Affiliations

  1. Lehrstuhl fuer Nachrichetntechnik, Ruhr Universitaet, 44780, Bochum, Germany

    Alfred Fettweis

  2. National Science Foundation, Arlington, VA, 22101, USA

    Sankar Basu

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  1. Alfred Fettweis
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  2. Sankar Basu
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Correspondence to Sankar Basu.

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Any opinion, finding, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

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Fettweis, A., Basu, S. Multidimensional causality and passivity of linear and nonlinear systems arising from physics. Multidim Syst Sign Process 22, 5–25 (2011). https://doi.org/10.1007/s11045-010-0135-y

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  • DOI: https://doi.org/10.1007/s11045-010-0135-y

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