Computing Invariant Zeros of a Linear System Using State-Space Realization
Links to Files
Author/Creator
Author/Creator ORCID
Date
Type of Work
Department
Program
Citation of Original Publication
Rights
Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
Subjects
Abstract
It is well known that zeros and poles of a single-input, single-output system in the transfer function form are the roots of the transfer function’s numerator and the denominator polynomial, respectively. However, in the state-space form, where the poles are a subset of the eigenvalue of the dynamics matrix and thus can be computed by solving an eigenvalue problem, the computation of zeros is a non-trivial problem. This paper presents a realization of a linear system that allows the computation of invariant zeros by solving a simple eigenvalue problem. The result is valid for square multi-input, multi-output (MIMO) systems, is unaffected by lack of observability or controllability, and is easily extended to wide MIMO systems. Finally, the paper illuminates the connection between the zero-subspace form and the normal form to conclude that zeros are the poles of the system’s zero dynamics.