Oscillation and convergence behaviours exhibited in an 'unstable' second-order digital filter with saturation-type non-linearity

Abstract

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.