Energyrelated concepts for nonlinear timevarying nport electrical networks: Passivity and losslessness
Abstract
Consistent definitions of passivity and losslessness are formulated which apply to nport electrical networks which are not necessarily linear, time variant, or lumped. Passively and losslessness conditions for nonlinear nports which can be mathematically represented by a finite order dynamical system verifiable without solving the state equation are found. A general theory is presented, consistent definitions of the concepts of passivity and losslessness are formulated, and various consequences of these definitions are presented and discussed. For the class of finite order dynamical systems, a number of significant results are obtained. The Smoothness Conjecture is shown to be false by producing a counterexample. Nontrivial sufficient and necessary algebraic conditions for passivity and losslessness are obtained. For first order time invariant dynamic systems, algebraic conditions for passivity and losslessness are obtained which are both necessary and sufficient. A complete, rigorous treatment of passivity and losslessness for linear time invariant finite order dynamical systems is presented.
 Publication:

Ph.D. Thesis
 Pub Date:
 March 1980
 Bibcode:
 1980PhDT........54G
 Keywords:

 Electric Networks;
 Energy Dissipation;
 Mathematical Models;
 Nonlinear Systems;
 Passivity;
 Algebra;
 Control Theory;
 Electron Density (Concentration);
 Equations Of State;
 Linear Systems;
 Optimal Control;
 Systems Analysis;
 Electronics and Electrical Engineering