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Computing Zeros of Linear Systems from State Space Matrices

Published on:

28 July 2023

Primary Category:

Optimization and Control

Paper Authors:

Jhon Manuel Portella Delgado,

Ankit Goel

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Key Details

Presents method to compute invariant zeros from state-space matrices

Transforms system into 'zero-subspace' form where zeros emerge

Shows zeros are eigenvalues of a partition of the transformed dynamics matrix

Allows computing zeros by solving a standard eigenvalue problem

Applies to square MIMO systems and is robust to minimality

AI generated summary

Computing Zeros of Linear Systems from State Space Matrices

This paper presents a technique to compute the invariant zeros of a linear system from its state-space realization. By transforming the system into a 'zero-subspace' form, the zeros are shown to be the eigenvalues of a partition of the transformed dynamics matrix. This allows computing zeros via an eigenvalue problem rather than a generalized eigenvalue problem. The result holds for square MIMO systems, is unaffected by lack of controllability/observability, and connects to the zero dynamics of the system.

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