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.
On the structure of the multivariable free response / Kavaja, J.; Piazzi, A.. - ELETTRONICO. - (2022), pp. 245-250. (Intervento presentato al convegno 2022 30th Mediterranean Conference on Control and Automation (MED) tenutosi a Athens, Greece nel June 28 - July 1, 2022) [10.1109/MED54222.2022.9837199].
On the structure of the multivariable free response
Kavaja J.;Piazzi A.
2022-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
