A new generalized energy criterion for the passivity of digital networks

A general passivity criterion for digital networks is introduced in this paper. Digital networks that meet this criterion form a stable and useful class of networks. The networks in this class have properties similar to passive analog networks. These networks are all stable, and some networks, including all linear networks, are shown to have restricted gain. The gain restriction can be used to design filters that are insensitive to changes in multiplier values at frequencies of maximum gain. Emerging directly from this criterion is a procedure for interconnecting simple networks to form a complex passive network. These networks remain stable after the introduction of rounding following multiplications so that these networks do not exhibit limit cycle oscillations. © 1997 IEEE.