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On stability of a class of positive linear functional difference equations

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Abstract

We first give a sufficient condition for positivity of the solution semigroup of linear functional difference equations. Then, we obtain a Perron–Frobenius theorem for positive linear functional difference equations. Next, we offer a new explicit criterion for exponential stability of a wide class of positive equations. Finally, we study stability radii of positive linear functional difference equations. It is proved that complex, real and positive stability radius of positive equations under structured perturbations (or affine perturbations) coincide and can be computed by explicit formulae.

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Authors and Affiliations

  1. The University of Electro-Communications, Chofu, Tokyo, 182-8585, Japan

    Pham Huu Anh Ngoc, Toshiki Naito & Jong Son Shin

Authors
  1. Pham Huu Anh Ngoc
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  2. Toshiki Naito
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  3. Jong Son Shin
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Correspondence to Pham Huu Anh Ngoc.

Additional information

Pham Huu Anh Ngoc and Toshiki Naito are supported by the Japan Society for Promotion of Science (JSPS) ID No. P 05049.

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Ngoc, P.H.A., Naito, T. & Shin, J.S. On stability of a class of positive linear functional difference equations. Math. Control Signals Syst. 19, 361–382 (2007). https://doi.org/10.1007/s00498-007-0018-4

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  • DOI: https://doi.org/10.1007/s00498-007-0018-4

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