New Results and Techniques for Computation of Stored Energy in Lossless/All-Pass Systems

Lossless and all-pass systems are energy-conservative in the sense that the energy that is extracted from the system always equals that supplied to the system. This stored energy turns out to be independent of the system realization/description. For example, there are different LC realizations of a lossless transfer function, but the energy stored can be uniquely expressed in terms of the port variables and their derivatives. This paper proposes new results and algorithms to compute the stored energy in lossless systems. We present four different techniques to compute the stored energy of lossless/all-pass systems. The first method is LC realization based (Foster, Cauer and their combinations) and the second is based on the Bezoutian of two polynomials. The notion of "balancing controllability/observability Gramians" is used for the third, while the last method is based on adjoint networks. A comparative study among the four methods shows that the first three methods are comparable with respect to computation time, while for numerical accuracy, the Bezoutian method is the best. Three different methods to compute the Bezoutian is also reported here: Euclidean long division, Pseudo-inverse method and the two dimensional discrete Fourier transform