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Sharp partial order and linear autonomous systems

Author

Listed:
  • Herrero, A.
  • Thome, N.

Abstract

This paper deals with autonomous linear systems and the sharp partial order. Given an autonomous linear system, we find another system, which is related to the first one by means of the sharp partial order. This relation can be interpreted in different ways: as a perturbation or as a projection of the initial system. Both points of view allow us to work with a new system with some previously selected behaviour. The solutions of the two systems are related via a matrix that gives the gap between them. We design some algorithms and analize their performance with numerical examples.

Suggested Citation

  • Herrero, A. & Thome, N., 2020. "Sharp partial order and linear autonomous systems," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    • Handle: RePEc:eee:apmaco:v:366:y:2020:i:c:s0096300319307283
    DOI: 10.1016/j.amc.2019.124736
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    References listed on IDEAS

    as
    1. Rakić, Dragan S. & Djordjević, Dragan S., 2015. "Star, sharp, core and dual core partial order in rings with involution," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 800-818.
    2. Mosić, Dijana & Cvetković-Ilić, Dragana S., 2016. "Some orders for operators on Hilbert spaces," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 229-237.
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    Cited by:

    1. Wang, Hongxing & Liu, Xiaoji, 2021. "Solutions of the matrix inequality AXA≤?A in some partial orders," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    2. Coll, C. & Herrero, A. & Sánchez, E. & Thome, N., 2020. "On the minus partial order in control systems," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    3. Baksalary, Oskar Maria & Trenkler, Götz, 2021. "On formulae for the Moore–Penrose inverse of a columnwise partitioned matrix," Applied Mathematics and Computation, Elsevier, vol. 403(C).

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    1. Coll, C. & Herrero, A. & Sánchez, E. & Thome, N., 2020. "On the minus partial order in control systems," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    2. Mosić, Dijana & Djordjević, Dragan S., 2015. "Weighted pre-orders involving the generalized Drazin inverse," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 496-504.

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