Title

Extremal values of differential equations with application to control systems

Journal title

Bulletin of the Polish Academy of Sciences Technical Sciences

Yearbook

2021

Volume

69

Issue

No. 1

Authors

Górecki, Henryk ; Zaczyk, Mieczysław

Affiliation

Górecki, Henryk : AGH University of Science and Technology, Department of Automatics and Robotics, Al. Mickiewicza 30, 30-059 Kraków, Poland ; Zaczyk, Mieczysław : AGH University of Science and Technology, Department of Automatics and Robotics, Al. Mickiewicza 30, 30-059 Kraków, Poland

Keywords

extremal values ; characteristic equation ; transfer function ; Dirac’s impulse ; multiple root

Divisions of PAS

Nauki Techniczne

Coverage

e136041

Bibliography

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 28^th 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 Graeffe- Lobactievsky”, 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).

Date

26.01.2021

Type

Article

Identifier

DOI: 10.24425/bpasts.2021.136041

Source

Bulletin of the Polish Academy of Sciences: Technical Sciences; 2021; 69; No. 1; e136041