On the structure of the multivariable free response

The structure of the free (or zero-input) response of multivariable (MIMO) linear time-invariant systems is investigated. In a behavioral setting, the free response is an autonomous behavior, solution of a homogeneous differential equation. A new closed-form expression of this solution is presented....

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Bibliographic Details
Main Authors: Kavaja, Juxhino, Piazzi, Aurelio
Format: Conference Proceeding
Language:English
Subjects:
Automation
Behavioral sciences
Closed-form solutions
Differential equations
Linear systems
Modal analysis
Time-domain analysis
Online Access:Request full text
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Summary:The structure of the free (or zero-input) response of multivariable (MIMO) linear time-invariant systems is investigated. In a behavioral setting, the free response is an autonomous behavior, solution of a homogeneous differential equation. A new closed-form expression of this solution is presented. It is a linear (real) combination of modes associated to the system's pole minimal polynomial. The vector coefficients of the modes belong to the output mode subspaces. These are characterized by a chain of subspace inclusions for each distinct pole. In the special, but relevant case of the pole minimal polynomial having simple roots the closed-form expression simplifies and admits a phasor interpretation. Examples are included to highlight the paper's findings.
ISSN:2473-3504
DOI:10.1109/MED54222.2022.9837199