Title :
Hopf bifurcation in discrete-time systems via a frequency domain approach
Author :
D´Amico, Maria Belen ; Moiola, Jorge L. ; Paolini, Eduardo E.
Author_Institution :
Dept. de Ingenieria Electr., Univ. Nacional del Sur, Bahia Blanca, Argentina
Abstract :
The application of the Hopf bifurcation theorem (HBT) for maps is presented in this paper. The invariant cycle emerging from the bifurcation is approximated using an analogous version of the graphical Hopf theorem (GHT) for continuous-time systems. This technique is formulated in the so-called frequency domain and it involves the use of the Nyquist stability criterion for discrete-time systems. An application example is included for illustration
Keywords :
Nyquist stability; bifurcation; discrete time systems; frequency-domain analysis; nonlinear control systems; nonlinear dynamical systems; Hopf bifurcation; Nyquist stability criterion; discrete-time systems; frequency domain approach; invariant cycle; Bifurcation; Delay; Feedback; Frequency domain analysis; Heterojunction bipolar transistors; Instruments; Limit-cycles; Nonlinear equations; Stability criteria; Transmission line matrix methods;
Conference_Titel :
Control of Oscillations and Chaos, 2000. Proceedings. 2000 2nd International Conference
Conference_Location :
St. Petersburg
Print_ISBN :
0-7803-6434-1
DOI :
10.1109/COC.2000.873974
