On passivity and power-balance inequalities of nonlinear RLC circuits

Arbitrary interconnections of passive (possibly nonlinear) resistors, inductors, and capacitors define passive systems, with power port variables the external source voltages and currents, and storage function the total stored energy. In this paper, we identify a class of RLC circuits (with convex energy function and weak electromagnetic coupling), for which it is possible to "add a differentiation" to the port terminals preserving passivity-with a new storage function that is directly related to the circuit power. To establish our results, we exploit the geometric property that voltages and currents in RLC circuits live in orthogonal spaces, i.e., Tellegen's theorem, and heavily rely on the seminal paper of Brayton and Moser (1964).