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Extremal values of differential equations with application to control systems

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Języki publikacji
EN
Abstrakty
EN
In the paper, maximal values xe(τ) of the solutions x(t) of the linear differential equations excited by the Dirac delta function are determined. The analytical solutions of the equations and also the maximal positive values of these solutions are obtained. The analytical formulae enable the design of the system with prescribed properties. The complementary case to the earlier paper is presented. In an earlier paper it was assumed that the roots si are different, and now we consider the case when s1=s2=...=sn.
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Strony
art. no. e136041
Opis fizyczny
Bibliogr. 16 poz., rys.
Twórcy
  • AGH University of Science and Technology, Department of Automatics and robotics, Al. Mickiewicza 30, 30-059 Kraków, Poland
  • AGH University of Science and Technology, Department of Automatics and robotics, Al. Mickiewicza 30, 30-059 Kraków, Poland
Bibliografia
  • [1] S. Białas, H. Górecki, and M. Zaczyk, “Extremal properties of the linear dynamic systems controlled by Dirac’s impulse”, J. Appl. Math. Comput. Sci. 30(1), 75‒81 (2020).
  • [2] L. Farina and S. Rinaldi: Positive Linear Systems. Theory and Application, J. Wiley, New York, 2000.
  • [3] H. Górecki and M. Zaczyk: “Design of the oscillatory systems with the extremal dynamic properties”, Bull. Pol. Ac.: Tech. 62(2), 241‒253 (2014).
  • [4] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
  • [5] K.L. Moore and S.P. Bhattacharyya, “A technique for choosing zero locations for minimal overshoot”, Proceedings of the 28th IEEE Conference on Decision and Control, Tampa, FL, USA 2, 1989, pp. 1230‒1233.
  • [6] H. Górecki and M. Zaczyk, “Positive extremal values and solutions of the exponential equations with application to automatics”, Bull. Pol. Ac.: Tech. 68(3), 585‒591 (2020).
  • [7] H. Górecki and M. Zaczyk, “Extremal dynamic errors in linear dynamic systems”, Bull. Pol. Ac.: Tech. 58(1), 99‒105 (2010).
  • [8] H. Górecki and S. Białas, “Relations between roots and coefficients of the transcendental equations”, Bull. Pol. Ac.: Tech. 58(4), 631‒634 (2010).
  • [9] H. Górecki and M. Zaczyk, “Design of systems with extremal dynamic properties”, Bull. Pol. Ac.: Tech. 61(3), 563‒567 (2013).
  • [10] S. Białas and H. Górecki, “Generalization of Vieta’s formulae to the fractional polynomials, and generalizations the method of GraeffeLobactievsky”, Bull. Pol. Ac.: Tech. 58(4), 625‒629 (2010).
  • [11] T. Kaczorek, “A new method for determination of positive realizations of linear continuous-time systems”, Bull. Pol. Ac.: Tech. 66(5), (2018).
  • [12] T. Kaczorek, “Global stability of nonlinear feedback systems with positive descriptor linear part”, Bull. Pol. Ac.: Tech. 67(1), 45‒51 (2019).
  • [13] T. Kaczorek, “Stability of interval positive continuous-time linear systems”, Bull. Pol. Ac.: Tech. 66(1), 31‒35 (2018).
  • [14] J. Osiowski, An outline of operator calculus. Theory and applications in electrical engineering, WNT, Warszawa, 1965 [in Polish].
  • [15] H. Górecki, Optimization and Control of Dynamic Systems, Springer, 2018.
  • [16] D.C. Kurtz, “Condition for all the roots of a polynomial to be real”, The American Mathematical Monthly 99(3), 259‒263 (1992).
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-d41e81f6-f5a6-4872-b95b-585722dae2c6
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