A new criterion for the overflow stability of second-order state-space digital filters using saturation arithmetic

Two recent approaches (one due to Singh [1990] and the other due to Liu and Michel [1992]) for the elimination of zero-input overflow oscillations in state-space digital filters designed with saturation arithmetic are compared. It is demonstrated that Singh's approach leads to a relatively less stringent condition for the nonexistence of overflow oscillations. Using Singh's approach, an improved version of Ritzerfeld-Werter's criterion for the nonexistence of overflow oscillations in second-order state-space digital filters is made available. Finally, a new zero-input limit cycle-free realizability condition for a generalized overflow characteristic is presented.