Positive extremal values and solutions of the exponential equations with application to automatics

• Autorzy: Górecki H. , Zaczyk M.

Identyfikatory

DOI

10.24425/bpasts.2020.133376

• 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. There are obtained the analytical solutions of the equations and also the maximal positive values of these solutions. The obtained sufficient conditions of the positivity of these solutions are defined by the Theorems. There are also formulated the necessary conditions of the positivity of these solutions. The analytical formulae enable the design of the system with prescribed properties.

Słowa kluczowe

EN

extremal values; transfer function; transcendental equations

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2020
• Tom: Vol. 68, nr 3
• Strony: 585--591
• Opis fizyczny: Bibliogr. 12 poz., rys.

Twórcy

autor

Górecki H.

• AGH University of Science and Technology, Department of Automatics and Robotics, al. Mickiewicza 30, 30-059 Kraków, Poland

autor

Zaczyk M.

• AGH University of Science and Technology, Department of Automatics and Robotics, al. Mickiewicza 30, 30-059 Kraków, Poland

Bibliografia

• [1] J. Osiowski, An outline of operator calculus. Theory and applications in electrical engineering, WNT, Warszawa, 1965 [in Polish].
• [2] S. Białas, H. Górecki, and M. Zaczyk, “Extremal properties of the linear dynamic systems controlled by Dirac’s impulse”, Int. J. Appl. Math. Comput. Sci. 30 (1), 75–81 (2020).
• [3] H. Górecki, and M. Zaczyk, “Design of systems with extremal dynamic properties”, Bull. Pol. Ac.: Tech. 61 (3), 563–567 (2013).
• [4] H. Górecki, Optimization and Control of Dynamic Systems, Springer, 2018.
• [5] L. Farina, and S. Rinaldi, Positive Linear Systems. Theory and Application, J. Wiley, New York, 2000.
• [6] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
• [7] T. Kaczorek, “A new method for determination of positive realizations of linear continuous-time systems”, Bull. Pol. Ac.: Tech. 66 (5), 605–611 (2018).
• [8] T. Kaczorek, “Global stability of nonlinear feedback systems with positive descriptor linear part”, Bull. Pol. Ac.: Tech. 67 (1), 45–51 (2019).
• [9] T. Kaczorek, “Stability of interval positive continuous-time linear systems”, Bull. Pol. Ac.: Tech. 66 (1), 31–35 (2018).
• [10] L. Benvenuti, and L. Farina, “A tutorial on the positive realization problem”, IEEE Trans. Autom. Control 49 (5), 651–664 (2004)
• [11] A. Rantzer, “On the Kalman-Yakubovich-Popov lemma for positive systems”, IEEE Trans. Autom. Control 61 (5), 1346–1349 (2016).
• [12] K. Sato and A. Takeda, “Construction methods of the nearest positive system”, IEEE Control Syst. Lett. 4 (1), 97–102 (2020).

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).