Frequency-Domain Criterion for the Global Stability of Dynamical Systems with Prandtl Hysteresis Operator
- 3 Downloads
In the present paper, dynamical systems with Prandtl hysteresis operator are considered. For the class of dynamical systems under consideration, a frequency-domain global stability criterion is formulated and proved. For a second-order dynamical system with Prandtl operator, we demonstrate the advantage of the obtained criterion as compared to the well-known criterion derived by Logemann and Ryan.
Keywordsdynamical systems hysteresis Prandtl operator stop operator frequency-domain stability criteria
Unable to display preview. Download preview PDF.
- 1.A. A. Andronov and N. N. Bautin, “On a degenerate case of the general problem of direct control,” Dokl. Akad. Nauk SSSR 46, 304–307 (1945).Google Scholar
- 2.A. A. Feldbaum, “The simplest relay systems of automatic control,” Autom. Telemekh. 10, 249–260 (1949).Google Scholar
- 3.A. A. Andronov, A. A. Witt, and S. E. Khaikin, Theory of Oscillations, 2nd ed., Ed. by N. Zheleztsov (Fizmatgiz, Moscow, 1959) [in Russian].Google Scholar
- 4.L. Prandtl, “Spannungsverteilung in plastischen körpern,” in Proc. 1st Int. Congr. for Applied Mechanics, Delft, 1924 (Waltman, Delft, 1925), pp. 43–54.Google Scholar
- 5.A. Visintin, Differential Models of Hysteresis, Ed. by F. John, J. E. Marsden, L. Sirovich (Springer-Verlag, New York, 1994).Google Scholar
- 7.A. Visintin, “Mathematical models of hysteresis,” in The Science of Hysteresis, Vol. 1: Mathematical Modeling and Applications, Ed. by G. Berotti and I. D. Mayergoyz (Academic, Oxford, 2006), pp. 1–114.Google Scholar
- 16.H. Logemann and A. D. Mawby, “Low-gain integral control of infinite-dimensional regular linear systems subject to input hysteresis,” in Advances in Mathematical Systems Theory: A Volume in Honor of Diederich Hinrichsen, Ed. by F. Colonius, U. Helmke, D. Prätzel-Wolters, and F. Wirth (Birkhäuser, Boston, 2000), pp. 255–293.Google Scholar