Jacob, Birgit (Delft Univ. of Tech.), Morris, Kirsten (Univ. of Waterloo), Trunk, Carsten (Tech. Univ. Berlin)

Minimum-Phase Behaviour of Damped Second-Order Systems

Scheduled for presentation during the Mini-Symposium "Distributed Parameter Systems-IV: Frequency Domain Approaches" (ThA06), Thursday, July 27, 2006, 11:40−12:05, Room G

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 19, 2024

Abstract

A stable finite-dimensional system is minimum phase or outer if and only if its transfer function has no zeros in the right-half-plane. A more general definition of minimum-phase systems exists for infinite-dimensional systems. As for finite-dimensional systems, it is desirable for a number of reasons that the system is minimum-phase. It is therefore advantageous to establish conditions under which infinite-dimensional systems are minimum-phase. Unfortunately, determining minimum-phase behaviour is less straightforward than for finite-dimensional systems.

The major focus of this work is to show that a large class of second-order systems, equipped with position measurements, are minimum-phase. These systems do not have positive real transfer functions, even in the finite-dimensional case. Writing the system in first-order form,the governing semigroup is a contraction, although not necessarily exponentially stable. We show that with certain assumptions on the damping operator, these systems are well-posed and stable. They also have finite relative degree. This is used to show that they are minimum-phase. The results are illustrated with an example of boundary control of a plate