Energy-Related Concepts for Nonlinear Time-Varying N-Ports: Passivity and Losslessness.

Definitions of passivity and losslessness are presented which apply to n-port networks which are not necessarily linear, time-invariant, or lumped in fact, these definitions apply to any n-port which has a dynamical system representation. For lumped, nonlinear n-port networks which can be mathematically represented by a finite-order dynamical system, conditions for passivity and losslessness are formulated in terms of properties of the state equation function, the output function, etc. These conditions can be verified without solving the state equation, and can be viewed as nonlinear generalizations of the well-known time-domain and frequency-domain passivity and losslessness conditions for linear time-invariant lumped n-port networks. Author