TY - GEN

T1 - Computing Invariant Zeros of a Linear System Using State-Space Realization

AU - Portella Delgado, Jhon Manuel

AU - Goel, Ankit

N1 - Publisher Copyright:
© 2024 AACC.

PY - 2024

Y1 - 2024

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85204424967&partnerID=8YFLogxK

U2 - 10.23919/ACC60939.2024.10644992

DO - 10.23919/ACC60939.2024.10644992

M3 - Conference contribution

AN - SCOPUS:85204424967

T3 - Proceedings of the American Control Conference

SP - 2746

EP - 2751

BT - 2024 American Control Conference, ACC 2024

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2024 American Control Conference, ACC 2024

Y2 - 10 July 2024 through 12 July 2024

ER -