Zero Dynamics for Port-Hamiltonian Systems

TL;DR

This paper characterizes the zero dynamics of port-Hamiltonian systems, showing they are well-defined and also port-Hamiltonian, with a constructive method for large systems, including wave equations on networks.

Contribution

It provides a complete characterization of zero dynamics for port-Hamiltonian systems with invertible feedthrough, extending understanding to systems with commensurate wave speeds.

Findings

Zero dynamics are port-Hamiltonian for systems with invertible feedthrough.

Zero dynamics are well-defined for systems with commensurate wave speeds.

A constructive procedure for calculating zero dynamics in large systems is developed.

Abstract

The zero dynamics of infinite-dimensional systems can be difficult to characterize. The zero dynamics of boundary control systems are particularly problematic. In this paper the zero dynamics of port-Hamiltonian systems are studied. A complete characterization of the zero dynamics for a port-Hamiltonian systems with invertible feedthrough as another port-Hamiltonian system on the same state space is given. It is shown that the zero dynamics for any port-Hamiltonian system with commensurate wave speeds are well-defined, and are also a port-Hamiltonian system. Examples include wave equations with uniform wave speed on a network. A constructive procedure for calculation of the zero dynamics, that can be used for very large system order, is provided.