A new condition for the elimination of overflow oscillations in direct form digital filters

This article proposes a new condition for the elimination of overflow oscillations in direct form digital filters with external interference. This condition reduces the effect of external interference to an ℋ∞ norm constraint. When there is no external interference, this condition ensures exponential stability. Moreover, this condition guarantees that the state vector is bounded if the external interference is bounded. The proposed condition is represented by linear matrix inequality (LMI), which can be checked easily by standard numerical packages. A numerical example is given to show the effectiveness of the proposed condition.