Advances in the Theory and Applications of Non-integer Order Systems, 1st Edition

  • Published By:
  • ISBN-10: 3319009338
  • ISBN-13: 9783319009339
  • DDC: 515.83
  • Grade Level Range: College Freshman - College Senior
  • 325 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

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This volume presents various aspects of non-integer order systems, also known as fractional systems, which have recently attracted an increasing attention in the scientific community of systems science, applied mathematics, control theory. Non-integer systems have become relevant for many fields of science and technology exemplified by the modeling of signal transmission, electric noise, dielectric polarization, heat transfer, electrochemical reactions, thermal processes,  acoustics, etc. The content is divided into six parts, every of which considers one of the currently relevant problems. In the first part the Realization problem is discussed, with a special focus on positive systems. The second part considers stability of certain classes of non-integer order systems with and without delays. The third part is focused on such important aspects as controllability, observability and optimization especially in discrete time. The fourth part is focused on distributed systems where non-integer calculus leads to new and interesting results. The next part considers problems of solutions and approximations of non-integer order equations and systems. The final and most extensive part is devoted to applications. Problems from mechatronics, biomedical engineering, robotics and others are all analyzed and solved with tools from fractional systems. This volume came to fruition thanks to high level of talks and interesting discussions at RRNR 2013 - 5th Conference on Non-integer Order Calculus and its Applications that took place at AGH University of Science and Technology in Kraków, Poland, which was organized by the Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering.

Table of Contents

Front Cover.
Other Frontmatter.
Title Page.
Copyright Page.
1: Realization Problem.
2: Realization Problem for Descriptor Positive Fractional Continuous-Time Linear Systems.
3: Positive Stable Minimal Realization of Fractional Discrete-Time Linear Systems.
4: Stability.
5: Frequency Domain Method for Stability Analysis of Linear Continuous-Time State-Space Systems with Double Fractional Orders.
6: Stability of Fractional Difference Systems with Two Orders.
7: Stability Conditions of Fractional Discrete-Time Scalar Systems with Two Delays.
8: Controllability, Observability and Optimal Control.
9: Constrained Controllability of h-difference Linear Systems with Two Fractional Orders.
10: Observability of Positive Fractional-Order Discrete-Time Systems.
11: Optimal Control Problem for Fractional Dynamic Systems–Linear Quadratic Discrete-Time Case.
12: Distributed Parameter Systems.
13: Stabilization of Wave Equation Using Standard/Fractional Derivative in Boundary Damping.
14: Fundamental Solutions to the Central Symmetric Space-Time Fractional Heat Conduction Equation and Associated Thermal Stresses.
15: Variable Order Fractional Isoperimetric Problem of Several Variables.
16: Mittag-Leffler Pattern in Anomalous Diffusion.
17: Solutions and Approximations.
18: Piecewise Affine Representation of Discrete in Time, Non-integer Order Systems.
19: Exact Solution of Two-Term Nonlinear Fractional Differential Equation with Sequential Riemann-Liouville Derivatives.
20: Laguerre Polynomial Approximation of Fractional Order Linear Systems.
21: Solutions of Systems with Two-Terms Fractional Difference Operators.
22: Comparison of h-Difference Fractional Operators.
23: Applications.
24: Reflection Symmetry in Fractional Calculus — Properties and Applications.
25: A General Fractional-Order Thermal Model for Buildings and Its Properties.
26: Heat Transfer Modeling in Ceramic Materials Using Fractional Order Equations.
27: A Comparative Study of ρIλDμ Controller Approximations Exemplified by Active Magnetic Levitation System.
28: The Application of Fractional Order Differential Calculus for the Description of Temperature Profiles in a Granular Layer.
29: Fractional-Order P2Dβ Controller for Uncertain Parameter DC Motor.
30: Synchronization of the Chaotic Ikeda Systems of Fractional Order.
31: Analog Modeling of Fractional Switched-Order Derivatives: Experimental Approach.
32: Fractional-Order Models of the Ultracapacitors.
33: Non-integer Order PIαDμ Control ICU-MM.
34: Comparison of Fractional- and Integer-Order Filters in Filtration of Myoelectric Activity Acquired from Biceps Brachii.
35: Variable-, Fractional-Order Dead-Beat Control of a Robot Arm.
Author Index.