Available Energy of Proper LLTIP One-Ports

A method for evaluating the available energy (as defined in 1981 by Wyatt ) of the proper linear lumped time-invariant passive one-ports of any order is proposed. The devised approach borrows many tools and techniques from the calculus of variations (Euler-Lagrange equations and natural transversality conditions). However, the final formula of the available energy has the simple structure of a quadratic form in the one-port state vector. To illustrate the method and the related energy matching problem, two numerical examples (one first-order and one second-order one-port) are discussed in detail.