Dissipativity analysis of negative resistance circuits

Abstract

This paper deals with the analysis of nonlinear circuits that interconnect passive elements (capacitors, inductors, and resistors) with nonlinear resistors exhibiting a range of $negative$ resistance. Such active elements are necessary to design circuits that switch and oscillate. We generalize the classical passivity theory of circuit analysis to account for such non-equilibrium behaviors. The approach closely mimics the classical methodology of (incremental) dissipativity theory, but with dissipation inequalities that combine $signed$ storage functions and $signed$ supply rates to account for the mixture of passive and active elements.