Controllability and Observability Results of an Implicit Type Fractional Order Delay Dynamical System
dc.contributor.author | Ahmad, Irshad | |
dc.contributor.author | Ahmad, Saeed | |
dc.contributor.author | ur Rahman, Ghaus | |
dc.contributor.author | Ahmad, Shabir | |
dc.contributor.author | De la Sen Parte, Manuel | |
dc.date.accessioned | 2022-12-20T14:31:34Z | |
dc.date.available | 2022-12-20T14:31:34Z | |
dc.date.issued | 2022-11-26 | |
dc.identifier.citation | Mathematics 10(23) : (2022) // Article ID 4466 | es_ES |
dc.identifier.issn | 2227-7390 | |
dc.identifier.uri | http://hdl.handle.net/10810/58902 | |
dc.description.abstract | Recently, several research articles have investigated the existence of solutions for dynamical systems with fractional order and their controllability. Nevertheless, very little attention has been given to the observability of such dynamical systems. In the present work, we explore the outcomes of controllability and observability regarding a differential system of fractional order with input delay. Laplace and inverse Laplace transforms, along with the Mittage–Leffler matrix function, are applied to the proposed dynamical system in Caputo’s sense, and a general solution is obtained in the form of an integral equation. Then, we set out conditions for the controllability of the underlying model, regarding the linear case. We then expound controllability conditions for the nonlinear case by utilizing the fixed point result of Schaefer and the Arzola–Ascoli theorem. Using the fixed point concept, we prove the observability of the linear case using the observability Grammian matrix. The necessary and sufficient conditions for the nonlinear case are investigated with the help of the Banach contraction mapping theorem. Finally, we add some examples to elaborate on our work. | es_ES |
dc.description.sponsorship | The APC is supported by the Basque Government, Grant IT1555-22. | es_ES |
dc.language.iso | eng | es_ES |
dc.publisher | MDPI | es_ES |
dc.rights | info:eu-repo/semantics/openAccess | es_ES |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
dc.subject | controllability | es_ES |
dc.subject | observability | es_ES |
dc.subject | grammian matrix | es_ES |
dc.subject | fractional differential equations | es_ES |
dc.subject | fixed point theorem | es_ES |
dc.title | Controllability and Observability Results of an Implicit Type Fractional Order Delay Dynamical System | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.date.updated | 2022-12-09T20:23:18Z | |
dc.rights.holder | © 2022 by the authors.Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/ 4.0/). | es_ES |
dc.relation.publisherversion | https://www.mdpi.com/2227-7390/10/23/4466 | es_ES |
dc.identifier.doi | 10.3390/math10234466 | |
dc.departamentoes | Electricidad y electrónica | |
dc.departamentoeu | Elektrizitatea eta elektronika |
Files in this item
This item appears in the following Collection(s)
Except where otherwise noted, this item's license is described as © 2022 by the authors.Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/ 4.0/).