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On the Canonical Form of Singular Distributed Parameter Systems

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Publicado en:Axioms vol. 14, no. 8 (2025), p. 583-597
Autor principal: Meng Zhongchen
Otros Autores: Jiang Yushan, Nier, Dong, Wang Wanyue, Chang Yunxiao, Ma Ruoxiang
Publicado:
MDPI AG
Materias:
Partial differential equations
Classification
Standardization
Temperature control
Variables
Distributed control systems
Distributed parameter systems
Matrix theory
Eigenvalues
Algebra
Canonical forms
Subsystems
Differential equations
Reynolds number
Acceso en línea:Citation/Abstract
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Resumen:This study addresses the standardization of Singular Distributed Parameter Systems (SDPSs). It focuses on classifying and simplifying first- and second-order linear SDPSs using characteristic matrix theory. First, the study classifies first-order linear SDPSs into three canonical forms based on characteristic curve theory, with an example illustrating the standardization process for parabolic SDPSs. Second, under regular conditions, first-order SDPSs can be decomposed into fast and slow subsystems, where the fast subsystem reduces to an Ordinary Differential Equation (ODE) system, while the slow subsystem retains the spatiotemporal characteristics of the original system. Third, the standardization and classification of second-order SDPSs is proposed using three reversible transformations that achieve structural equivalence. Finally, an illustrative example of a building temperature control is built with SDPSs. The simulation results show the importance of system standardization in real-world applications. This research provides a theoretical foundation for SDPS standardization and offers insights into the practical implementation of distributed temperature systems.
ISSN:2075-1680
DOI:10.3390/axioms14080583
Fuente:Engineering Database