Ebook: Advances in the Theory and Applications of Non-integer Order Systems: 5th Conference on Non-integer Order Calculus and Its Applications, Cracow, Poland

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.

---

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 Krak?w, Poland, which was organized by the Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering.

---

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 Krak?w, Poland, which was organized by the Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering.

Content:
Front Matter....Pages 1-13
Front Matter....Pages 1-1
Realization Problem for Descriptor Positive Fractional Continuous-Time Linear Systems....Pages 3-14
Positive Stable Minimal Realization of Fractional Discrete-Time Linear Systems....Pages 15-27
Front Matter....Pages 29-29
Frequency Domain Method for Stability Analysis of Linear Continuous-Time State-Space Systems with Double Fractional Orders....Pages 31-39
Stability of Fractional Difference Systems with Two Orders....Pages 41-52
Stability Conditions of Fractional Discrete-Time Scalar Systems with Two Delays....Pages 53-64
Front Matter....Pages 65-65
Constrained Controllability of h-Difference Linear Systems with Two Fractional Orders....Pages 67-75
Observability of Positive Fractional-Order Discrete-Time Systems....Pages 77-86
Optimal Control Problem for Fractional Dynamic Systems – Linear Quadratic Discrete-Time Case....Pages 87-97
Front Matter....Pages 99-99
Stabilization of Wave Equation Using Standard/Fractional Derivative in Boundary Damping....Pages 101-121
Fundamental Solutions to the Central Symmetric Space-Time Fractional Heat Conduction Equation and Associated Thermal Stresses....Pages 123-132
Variable Order Fractional Isoperimetric Problem of Several Variables....Pages 133-139
Mittag-Leffler Pattern in Anomalous Diffusion....Pages 141-146
Front Matter....Pages 147-147
Piecewise Affine Representation of Discrete in Time, Non-integer Order Systems....Pages 149-159
Exact Solution of Two-Term Nonlinear Fractional Differential Equation with Sequential Riemann-Liouville Derivatives....Pages 161-170
Laguerre Polynomial Approximation of Fractional Order Linear Systems....Pages 171-182
Solutions of Systems with Two-Terms Fractional Difference Operators....Pages 183-189
Comparison of h-Difference Fractional Operators....Pages 191-197
Front Matter....Pages 199-199
Reflection Symmetry in Fractional Calculus – Properties and Applications....Pages 201-211
A General Fractional-Order Thermal Model for Buildings and Its Properties....Pages 213-220
Heat Transfer Modeling in Ceramic Materials Using Fractional Order Equations....Pages 221-229
Front Matter....Pages 199-199
The Application of Fractional Order Differential Calculus for the Description of Temperature Profiles in a Granular Layer....Pages 231-241
Synchronization of the Chaotic Ikeda Systems of Fractional Order....Pages 243-248
Analog Modeling of Fractional Switched-Order Derivatives: Experimental Approach....Pages 249-259
Fractional-Order Models of the Ultracapacitors....Pages 261-269
Comparison of Fractional- and Integer-Order Filters in Filtration of Myoelectric Activity Acquired from Biceps Brachii....Pages 271-280
Variable-, Fractional-Order Dead-Beat Control of a Robot Arm....Pages 281-293
Back Matter....Pages 295-303
....Pages 305-312