Title Advances in the theory and applications of non-integer order systems : 5th Conference on Non-integer Order Calculus and Its Applications, Cracow, Poland / Wojciech Mitkowski, Janusz Kacprzyk, Jerzy Baranowski, editors

Published Cham ; New York : Springer, ©2013

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Description 1 online resource (xv, 323 pages) Series Lecture notes in electrical engineering, 1876-1100 ; v. 257 Lecture notes in electrical engineering ; v. 257. Contents Realization Problem. Realization Problem for Descriptor Positive Fractional Continuous-Time Linear Systems / Tadeusz Kaczorek -- Positive Stable Minimal Realization of Fractional Discrete-Time Linear Systems / Łukasz Sajewski -- Stability. Frequency Domain Method for Stability Analysis of Linear Continuous-Time State-Space Systems with Double Fractional Orders / Mikołaj Busłowicz -- Stability of Fractional Difference Systems with Two Orders / Małgorzata Wyrwas, Ewa Girejko, Dorota Mozyrska, Ewa Pawłuszewicz -- Stability Conditions of Fractional Discrete-Time Scalar Systems with Two Delays / Andrzej Ruszewski -- Controllability, Observability and Optimal Control. Constrained Controllability of h-Difference Linear Systems with Two Fractional Orders / Ewa Pawłuszewicz, Dorota Mozyrska -- Observability of Positive Fractional-Order Discrete-Time Systems / Wojciech Trzasko -- Optimal Control Problem for Fractional Dynamic Systems -- Linear Quadratic Discrete-Time Case / Andrzej Dzieliński, Przemysław M. Czyronis -- Distributed Parameter Systems. Stabilization of Wave Equation Using Standard/Fractional Derivative in Boundary Damping / Piotr Grabowski Fundamental Solutions to the Central Symmetric Space-Time Fractional Heat Conduction Equation and Associated Thermal Stresses / Yuriy Povstenko -- Variable Order Fractional Isoperimetric Problem of Several Variables / Tatiana Odziehjewicz -- Mittag-Leffler Pattern in Anomalous Diffusion / Bartłomiej Dybiec -- Solutions and Approximations. Piecewise Affine Representation of Discrete in Time, Non-integer Order Systems / Stefan Domek -- Exact Solution of Two-Term Nonlinear Fractional Differential Equation with Sequential Riemann-Liouville Derivatives / Marek Błasik, Małgorzata Klimek -- Laguerre Polynomial Approximation of Fractional Order Linear Systems / Piotr Bania, Jerzy Baranowski -- Solutions of Systems with Two-Terms Fractional Difference Operators / Ewa Girejko, Dorota Mozyrska, Małgorzata Wyrwas -- Comparison of h-Difference Fractional Operators / Dorota Mozyrska, Ewa Girejko, Małgorzata Wyrwas -- Applications. Reflection Symmetry in Fractional Calculus -- Properties and Applications / Małgorzata Klimek, Maria Lupa -- A General Fractional-Order Thermal Model for Buildings and Its Properties / Pawel Skruch -- Heat Transfer Modeling in Ceramic Materials Using Fractional Order Equations / Anna Obrączka, Jakub Kowalski Preface; Contents; Part I Realization Problem; Realization Problem for Descriptor Positive Fractional Continuous-Time Linear Systems; 1 Introduction; 2 Positive Descriptor Fractional Systems and Decomposition of Transfer Matrices; 3 Positive Realizations of Transfer Matrices; 4 Positive Realizations of Strictly Proper Transfer Matrices; 5 Concluding Remarks; References; Positive Stable Minimal Realization of Fractional Discrete-Time Linear Systems; 1 Introduction; 2 Preliminaries and Problem Formulation; 3 Solution of Realization Problem; 3.1 General Transfer Matrix 3.2 L-bounded Transfer Matrix4 Concluding Remarks; References; Part II Stability; Frequency Domain Method for Stability Analysis of Linear Continuous-Time State-Space Systems with Double Fractional Orders; 1 Introduction; 2 Problem Formulation; 3 The Main Results; 4 Illustrative Examples; 5 Concluding Remarks; References; Stability of Fractional Difference Systems with Two Orders; 1 Introduction; 2 Preliminaries; 3 Description of Difference Systems with Two Orders; 4 Lyapunov Stability; 5 Conclusions; References; Stability Conditions of Fractional Discrete-Time Scalar Systems with Two Delays 1 Introduction2 Problem Formulation; 3 Solution of the Problem; 4 Concluding Remarks; References; Part III Controllability, Observability and Optimal Control; Constrained Controllability of h-Difference Linear Systems with Two Fractional Orders; 1 Introduction; 2 h-Fractional Difference; 3 Linear Control Systems with Two Orders; 4 Constrained Control; 5 Conclusions and Future Work; References; Observability of Positive Fractional-Order Discrete-Time Systems; 1 Introduction; 2 Linear Discrete-Time Fractional-Order Systems; 3 Observabilty of the Positive Systems; 4 Example; 5 Concluding Remarks 3.2 Examination of the Closed-Loop System3.3 Eigenvalues of the Closed-Loop State Operator; 4 Discussion and Conclusions; References; Fundamental Solutions to the Central Symmetric Space-Time Fractional Heat Conduction Equation and Associated Thermal Stresses; 1 Introduction; 2 Mathematical Preliminaries; 3 Statement and Solution of the Problem; 3.1 The First Cauchy Problem; 3.2 The Second Cauchy Problem; 3.3 The Source Problem; 4 Concluding Remarks; References; Variable Order Fractional Isoperimetric Problem of Several Variables; 1 Introduction; 2 Preliminaries Summary Presents novel advances in both the theory and applications of non-integer order systems. The main focus is on control and electrical engineering, biomedical engineering, and systems theory Analysis Engineering Physics Control Complexity Signal, Image and Speech Processing computerwetenschappen computer sciences beeldverwerking image processing spraak speech controle Engineering (General) Techniek (algemeen) Notes Includes author index Bibliography Includes bibliographical references and index Notes English Online resource; title from digital title page (viewed July 10, 2014) Subject Fractional calculus -- Congresses Dynamics -- Mathematics -- Congresses MATHEMATICS -- Calculus. MATHEMATICS -- Mathematical Analysis. Ingénierie. Dynamics -- Mathematics Fractional calculus Genre/Form proceedings (reports) Conference papers and proceedings Conference papers and proceedings. Actes de congrès. Form Electronic book Author Mitkowski, Wojciech. Kacprzyk, Janusz. Baranowski, Jerzy. ISBN 9783319009339 3319009338 331900932X 9783319009322

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