Available energy and passivity of first-order LLTI one-ports

The energy behavior of first-order linear lumped time-invariant one-ports is thoroughly investigated, starting from the definition of available energy introduced by Wyatt et al. in 1981 and exploiting the calculus of variations approach. First, all the extrema of the energy delivered from these components over finite time intervals are identified and evaluated. Then, available energy and passivity are inferred by comparing these results on the nonnegative time half-axis. The case of reducible one-ports, which is beyond the traditional criterion based on the theory of positive-real rational functions, is also treated. Two numerical circuital examples are used throughout this paper to illustrate the theoretical results obtained.