Energy‐related concepts for non‐linear time‐varying <i>n</i>‐ports: Passivity and losslessness

Abstract Definitions of passivity and losslessness are presented that apply to n ‐port networks which are not necessarily linear, time‐invariant, or lumped; in fact, these definitions apply to any n ‐port that has an abstract dynamical system representation. For lumped, non‐linear n ‐port networks that 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 non‐linear generalizations of the well‐known time‐domain and frequency‐domain passivity and losslessness conditions for linear time‐invariant lumped n ‐port networks.