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Energy‐related concepts for non‐linear time‐varying n ‐ports: Passivity and losslessness
Author(s) -
Gannett J. W.,
Chua L. O.
Publication year - 1981
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490090405
Subject(s) - passivity , lti system theory , port (circuit theory) , representation (politics) , control theory (sociology) , time domain , nonlinear system , mathematics , invariant (physics) , state (computer science) , function (biology) , linear system , computer science , mathematical analysis , engineering , algorithm , physics , electronic engineering , control (management) , artificial intelligence , law , mathematical physics , biology , quantum mechanics , evolutionary biology , political science , computer vision , politics , electrical engineering
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.