Autors: Kolev, L. V., Petrakieva, S. K.
Title: Assessing the stability of linear time-invariant interval dynamic systems
Keywords: robust stability analysis, eigenvalues of interval matrices,

Abstract: It is known that stability analysis of linear time-invariant dynamic systems under parameter uncertainties can be equated to estimating the range of the eigenvalues of matrices whose elements are intervals. In this paper, first, the problem of finding tight outer bounds on the eigenvalue ranges is considered. A method for computing such bounds is suggested which consists, essentially, of setting up and solving a system of n mildly nonlinear algebraic equations, n being the size of the interval matrix investigated. The main result of the paper, however, is a method for determining the right end-point of the exact eigenvalue ranges. The latter makes use of the outer bounds. It is applicable if certain computationally verifiable monotonicity conditions are fulfilled. The methods suggested can be applied for robust stability analysis of both continuous- and discrete-time systems. Numerical examples illustrating the applicability of the new methods are also provided.

References

    Issue

    IEEE Trans. on Automatic Control, vol. 50, issue 3, pp. 393 - 397, 2005, United States, DOI 0018-9286 , 1558-2523 , 2334-3303 / 10.1109/TAC.2005.843857

    Copyright IEEE Explore

    Цитирания (Citation/s):
    1. Hammouche, M., Lutz, P., Rakotondrabe, M., Robust and optimal output-feedback control for interval state-space model: Application to a two-degrees-of-freedom piezoelectric tube actuator, Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME 141(2),021008 - 2019 - в издания, индексирани в Scopus или Web of Science
    2. Mounir Hammouche, Abdenbi Mohand-Ousaid, Philippe Lutz, Micky Rakotondrabe, Robust Interval Luenberger Observer-Based State Feedback Control: Application to a Multi-DOF Micropositioner, Control Systems Technology IEEE Transactions on, vol. 27, no. 6, pp. 2672-2679 - 2019 - в издания, индексирани в Scopus или Web of Science
    3. Zhu M., Li D., Bases and dimension of interval vector space, Computational and Applied Mathematics, 2021, 40(1), art. no. 6, pp. - 2021 - в издания, индексирани в Scopus или Web of Science
    4. Masoud Pourasghar, Vicenç Puig, Carlos Ocampo-Martinez, On robust interval observer design for uncertain systems subject to both time-invariant and time-varying uncertainties, International Journal of Control, vol. 13, N 11, pp. 2577-2595, 2020. - 2020 - в издания, индексирани в Scopus или Web of Science
    5. Mounir Hammouche, Philippe Lutz, Micky Rakotondrabe, Robust and guaranteed output-feedback force control of piezoelectric actuator under temperature variation and input constraints, Asian Journal of Control, vol. 22, N 6, pp. 2242-2253, 2020. - 2020 - в издания, индексирани в Scopus или Web of Science
    6. Maiti, S., Chakraverty, Sn., Evolution of Interval Eigenvalue Problems and its Applications to the Uncertain Dynamic Problems, 2022, Archives of Computational Methods in Engineering, ISSN: 11343060, DOI: 10.1007/s11831-022-09837-1 https://www.scopus.com/record/display.uri?origin=citedby&eid=2-s2.0-85141648406&noHighlight=false&relpos=0 - 2022 - в издания, индексирани в Scopus или Web of Science
    7. V. Atanasov, D. Stoilov, E. Mechkov, Changes of iron losses during the service of distribution transformers, 14th Electrical Engineering Faculty Conference, BulEF’2022, Varna, Bulgaria, 14 – 17 September 2022, Code: 186442, ISBN: 978-166549026-9, DOI: 10.1109/BulEF56479.2022.10021176 https://ieeexplore.ieee.org/document/10021176 https://www.scopus.com/record/display.uri?eid=2-s2.0-85147845363&origin=resultslist&sort=plf-f&cite=2-s2.0-16244381788&src=s&imp=t&sid=2abb59bca99b66e9a1af4bbbafba6db4&sot=cite&sdt=a&sl=0&relpos=1&citeCnt=0&searchTerm= - 2022 - в издания, индексирани в Scopus или Web of Science
    8. Zerrouki D., Ouanes M., Bounds on eigenvalues of real symmetric interval matrices for αBB method in global optimization, 2024, Yugoslav Journal of Operations Research, vol. 34, Issue 1, pp. 73 – 92, ISSN: 03540243, DOI: 10.2298/YJOR230315019Z https://www.scopus.com/record/display.uri?origin=citedby&eid=2-s2.0-85187289020&noHighlight=false&relpos=0 - 2024 - в издания, индексирани в Scopus или Web of Science

    Вид: статия в списание, публикация в издание с импакт фактор, публикация в реферирано издание, индексирана в Scopus и Web of Science