Stabilization of Generalized Hamiltonian Systems

Canonical Transformation Approach

Abstract

The generalized Hamiltonian systems are generalization of well-known Hamiltonian systems, which include various passive electric circuit systems as well as mechanical ones. This paper introduces the canonical transformation for the generalized Hamiltonian systems, which preserves the Hamiltonian structure of the original system and is expected to provide new insights and useful tools for analysis and synthesis of such systems. First, the class of such transformations and some of their properties are clarified. Second, we show how to stabilize the generalized Hamiltonian systems by using the transformation. This method works even when we can not stabilize them by conventional unity feedback without canonical transformation. Furthermore, it is shown that the proposed stabilization method includes the well-known one which exploits the virtual potential energy.