Fundamentals of Differential Algebra
In this chapter the basics of differential algebra are briefly presented, which is a mathematical tool used in the design of controllers for linear and nonlinear systems. The concepts presented here will be used in the next chapters for fault diagnosis an
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Rafael Martínez-Guerra Fidel Meléndez-Vázquez Iván Trejo-Zúñiga
Fault-tolerant Control and Diagnosis for Integer and Fractional-order Systems Fundamentals of Fractional Calculus and Differential Algebra with Real-Time Applications
Studies in Systems, Decision and Control Volume 328
Series Editor Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland
The series “Studies in Systems, Decision and Control” (SSDC) covers both new developments and advances, as well as the state of the art, in the various areas of broadly perceived systems, decision making and control–quickly, up to date and with a high quality. The intent is to cover the theory, applications, and perspectives on the state of the art and future developments relevant to systems, decision making, control, complex processes and related areas, as embedded in the fields of engineering, computer science, physics, economics, social and life sciences, as well as the paradigms and methodologies behind them. The series contains monographs, textbooks, lecture notes and edited volumes in systems, decision making and control spanning the areas of Cyber-Physical Systems, Autonomous Systems, Sensor Networks, Control Systems, Energy Systems, Automotive Systems, Biological Systems, Vehicular Networking and Connected Vehicles, Aerospace Systems, Automation, Manufacturing, Smart Grids, Nonlinear Systems, Power Systems, Robotics, Social Systems, Economic Systems and other. Of particular value to both the contributors and the readership are the short publication timeframe and the world-wide distribution and exposure which enable both a wide and rapid dissemination of research output. Indexed by SCOPUS, DBLP, WTI Frankfurt eG, zbMATH, SCImago. All books published in the series are submitted for consideration in Web of Science.
More information about this series at http://www.springer.com/series/13304
Rafael Martínez-Guerra Fidel Meléndez-Vázquez Iván Trejo-Zúñiga •
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Fault-tolerant Control and Diagnosis for Integer and Fractional-order Systems Fundamentals of Fractional Calculus and Differential Algebra with Real-Time Applications
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Rafael Martínez-Guerra Departamento de Control Automático CINVESTAV-IPN Ciudad de México, Mexico
Fidel Meléndez-Vázquez Departamento de Física y Matemáticas Universidad Iberoamericana Ciudad de México, Mexico
Iván Trejo-Zúñiga División de Mecatrónica y TIC Universidad Tecnológica de San Juan del Río San Juan del Río, Querétaro, Mexico
ISSN 2198-4182 ISSN 2198-4190 (electronic) Studies in Systems, Decision and Control ISBN 978-3-030-62093-6 ISBN 978-3-030-62094-3 (eBook) https://doi.org/10.1007/978-3-030-62094-3 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfil
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