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Oscillation and convergence behaviours exhibited in an ‘unstable’ second‐order digital filter with saturation‐type non‐linearity
Author(s) -
Ling Bingo WingKuen,
Ho Charlotte YukFan,
Leung Raymond ShingKeung,
Tam Peter KwongShun
Publication year - 2004
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.260
Subject(s) - linearity , saturation (graph theory) , mathematics , eigenvalues and eigenvectors , oscillation (cell signaling) , bifurcation , mathematical analysis , convergence (economics) , control theory (sociology) , digital filter , hopf bifurcation , type (biology) , filter (signal processing) , physics , nonlinear system , engineering , computer science , combinatorics , economics , ecology , control (management) , quantum mechanics , artificial intelligence , biology , electrical engineering , genetics , economic growth
This letter explains the oscillatory behaviours exhibited in a second‐order digital filter with saturation‐type non‐linearity via the Hopf bifurcation theorem. It is shown that depending on the bifurcation parameter, the state variables may converge to zero even when the eigenvalues of the system matrix are outside the unit circle. Copyright © 2004 John Wiley & Sons, Ltd. abstract