The causal α -exponential and the solution of fractional linear time-invariant systems
type: Item
instance of: scholarly article
title: The causal α -exponential and the solution of fractional linear time-invariant systems
zbMATH Open document ID: 1546.34008
DOI: 10.1080/00207721.2024.2321369
author: Gabriel Bengochea
author: Manuel Ortigueira
author: Luis Verde-Star
published in: International Journal of Systems Science. Principles and Applications of Systems and Integration
publication date: 2024-07-23T00:00:00Z
review text: The paper introduces an innovative approach to solving fractional linear systems using \(\alpha\)-exponential monomials, without the need for traditional integral transforms. This new method provides a direct solution, which simplifies the computational process and enhances efficiency and accuracy, particularly for large time values.\N\NThe key contribution of the paper is the development of a methodology that avoids the use of integral transforms, which are typically employed in solving fractional linear systems. Instead, the authors utilize \(\alpha\)-exponential monomials to provide a direct approach to solving these systems. This method is advantageous as it simplifies the computational process while maintaining a high level of accuracy. The research builds upon the foundational work of \textit{B. Shahrrava} [``Closed-form impulse responses of linear time-invariant systems: a unifying approach'', in: IEEE Signal Process. Mag. 35, No. 4, 126--132 (2018; \url{doi:10.1109/MSP.2018.2810300})] by extending the methodology to fractional cases and addressing both impulse and step responses. The approach effectively views the fractional system as a cascade connection of two systems, reducing the problem to finding the impulse response. This streamlined process is both innovative and practical.\N\NThe paper also addresses numerical accuracy and effectiveness by demonstrating that the proposed solution converges uniformly to a continuous function for positive time values. The authors employ the integral representation of the Mittag-Leffler function to overcome numerical issues associated with series solutions, which ensures the robustness of the method for large time values. This is a significant improvement over traditional methods, which often struggle with accuracy and convergence issues in such cases. Furthermore, the inclusion of practical examples and numerical simulations in the paper validates the effectiveness of the proposed method. The authors also provide MATL…
reviewed by: Ioannis K. Dassios
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 33E12
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34H05
Mathematics Subject Classification ID: 93C27
zbMATH DE Number: 7885487
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7885487