Regular Papers

International Journal of Control, Automation, and Systems 2024; 22(11): 3434-3447

https://doi.org/10.1007/s12555-024-0058-2

© The International Journal of Control, Automation, and Systems

On the Maximal Output Admissible Set for Linear Distributed Systems

Issam Khaloufi, Abdessamad Tridane*, Youssef Benfatah, and Mostafa Rachik

United Arab Emirates University

Abstract

This paper investigates the maximal output set for a class of linear distributed systems with discrete output. This exploration is novel, as previous studies primarily focused on localized systems. We define an initial state as output admissible if its corresponding output satisfies specified constraints. This set of initial states termed the maximal output set (MOS), is shown to be nonempty, bounded, and characterized by a finite number of inequalities under suitable assumptions. In addition to theoretical characterization, we propose an algorithmic approach. To illustrate our framework, we provide a numerical example involving a parabolic system. Furthermore, we apply our results to address a disturbance rejection problem, aiming to design feedback controls that ensure the robustness of the system’s output against disturbances.

Keywords Distributed linear systems, disturbance rejection, maximal output set, observability, robustness.

Article

Regular Papers

International Journal of Control, Automation, and Systems 2024; 22(11): 3434-3447

Published online November 1, 2024 https://doi.org/10.1007/s12555-024-0058-2

Copyright © The International Journal of Control, Automation, and Systems.

On the Maximal Output Admissible Set for Linear Distributed Systems

Issam Khaloufi, Abdessamad Tridane*, Youssef Benfatah, and Mostafa Rachik

United Arab Emirates University

Abstract

This paper investigates the maximal output set for a class of linear distributed systems with discrete output. This exploration is novel, as previous studies primarily focused on localized systems. We define an initial state as output admissible if its corresponding output satisfies specified constraints. This set of initial states termed the maximal output set (MOS), is shown to be nonempty, bounded, and characterized by a finite number of inequalities under suitable assumptions. In addition to theoretical characterization, we propose an algorithmic approach. To illustrate our framework, we provide a numerical example involving a parabolic system. Furthermore, we apply our results to address a disturbance rejection problem, aiming to design feedback controls that ensure the robustness of the system’s output against disturbances.

Keywords: Distributed linear systems, disturbance rejection, maximal output set, observability, robustness.

IJCAS
November 2024

Vol. 22, No. 11, pp. 3253~3544

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