Solution of the System Structure Reconstruction Problem Based on Generalization of Tellegen's Principle

Abstract

An extraordinary generality, conceptual simplicity and practical usefulness of the Tellegen's theorem is well known in the field of electrical engineering [1]. It is one of few general theoretical results that apply in non-linear and time-varying situations, too. For standard linear electrical network models with constant parameters many classical results of electrical circuits theory can be derived as direct consequences of it. In the paper a more general class of abstract strictly causal system representations is addressed. A new problem, that of the abstract state space system representation structure reconstruc-tion has been formulated in [3], and partially solved in [3] and [4]. In this paper a new approach based on a generalized form of the classical Tellegen's principle, providing an equivalence class of physically as well as mathematically correct solutions is developed and some well-known, as well as new results are shown to be straightforward consequences of the derived struc-ture. Some connections of dissipativity, conservativity, state and parameter minimality, instability and chaos with system representation structures are investigated from this point of view. Analytical results are illustrated by a number of typical examples and visualized by simulations