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A novel unified approach to invariance conditions for a linear dynamical system

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  • Horváth, Zoltán
  • Song, Yunfei
  • Terlaky, Tamás

Abstract

In this paper, we propose a novel, simple, and unified approach to explore sufficient and necessary conditions, i.e., invariance conditions, under which four classic families of convex sets, namely, polyhedra, polyhedral cones, ellipsoids, and Lorenz cones, are invariant sets for a linear discrete or continuous dynamical system.

Suggested Citation

  • Horváth, Zoltán & Song, Yunfei & Terlaky, Tamás, 2017. "A novel unified approach to invariance conditions for a linear dynamical system," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 351-367.
    • Handle: RePEc:eee:apmaco:v:298:y:2017:i:c:p:351-367
    DOI: 10.1016/j.amc.2016.10.007
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    References listed on IDEAS

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    1. Zoltán Horváth & Yunfei Song & Tamás Terlaky, 2016. "Invariance Conditions for Nonlinear Dynamical Systems," Springer Optimization and Its Applications, in: Boris Goldengorin (ed.), Optimization and Its Applications in Control and Data Sciences, pages 265-280, Springer.
    2. Polterovich, Victor & Popov, Vladimir, 2006. "Эволюционная Теория Экономической Политики: Часть I: Опыт Быстрого Развития [An Evolutionary Theory of Economic Policy: Part I: The Experience of Fast Development]," MPRA Paper 22168, University Library of Munich, Germany.
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    1. Yuyao Lei & Hongli Yang & Ivan Ganchev Ivanov, 2023. "Characterization of Positive Invariance of Quadratic Convex Sets for Discrete-Time Systems Using Optimization Approaches," Mathematics, MDPI, vol. 11(11), pages 1-18, May.

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