Contents -- Preface -- Acknowledgments -- List of Figures -- List of Tables -- 1. Fractional Order Systems -- 1.1 Fractional Order Differintegral Operator: Historical Notes -- 1.2 Preliminaries and Definitions -- 1.3 Laplace Transforms and System Representation -- 1.4 General Properties of the Fractional System -- 1.5 Impulse Response of a General Fractional System -- 1.6 Numerical Methods for Calculation of Fractional Derivatives and Integrals -- 1.7 Fractional LTI Systems -- 1.8 Fractional Nonlinear Systems -- 1.9 Stability of Fractional LTI Systems -- 1.10 Stability of Fractional Nonlinear Systems -- 2. Fractional Order PID Controller and their Stability Regions Definition -- 2.1 Introduction -- 2.2 ProblemCharacterization -- 2.3 Theory for Analyzing Systems with Time Delays -- 2.3.1 Hermite-Biehler Theorem -- 2.3.2 Pontryagin Theorem -- 2.4 Stability Regions with PIλDµ Controller -- 2.5 Results -- 3. Fractional Order Chaotic Systems -- 3.1 Introduction -- 3.2 Concept of Chua's System -- 3.2.1 Classical Chua's Oscillator -- 3.2.2 Chua-Hartley's Oscillator -- 3.2.3 Chua-Podlubny's Oscillator -- 3.2.4 New Fractional-Order Chua's Oscillator -- 3.2.4.1 Experimental Measurements -- 3.2.4.2 Simulation Results -- 3.3 Fractional-Order Van der Pol Oscillator -- 3.4 Fractional-Order Duffing's Oscillator -- 3.5 Fractional-Order Lorenz's System -- 3.6 Fractional-OrderGenesio-Tesi System -- 3.7 Fractional-Order Lu's System -- 3.8 Fractional-Order Rossler's System -- 3.9 Fractional-Order Newton-Leipnik System -- 3.10 Fractional-Order Lotka-Volterra System -- 3.11 Concept of Volta's System -- 3.11.1 Integer-Order Volta's System -- 3.11.2 Fractional-Order Volta's System -- 3.11.2.1 Case I: Commensurate Order -- 3.11.2.2 Case II: Incommensurate Order -- 4. Field Programmable Gate Array Implementation -- 4.1 Numerical Fractional Integration.

4.2 Grünwald-Letnikov Fractional Derivatives -- 4.3 The "Short-Memory" Principle -- 4.4 FPGA Hardware Implementation -- 4.4.1 FPGA Introduction -- 4.4.2 Remarks on the Fractional Differintegral Operator -- 4.4.3 FPGA Implementation of the Fractional Differintegral Operator -- 5. Microprocessor Implementation and Applications -- 5.1 Introduction -- 5.2 Fractional Controller Realized by PIC Processor -- 5.2.1 Fractional-Order Integrator -- 5.2.2 Measured Results -- 5.3 Temperature Control of a Solid by PC and PCL 812 -- 5.3.1 Model of Controlled System -- 5.3.2 Controller Parameters Design and Implementation -- 5.3.3 Experimental Setup and Results -- 5.4 Temperature Control of a Heater by PLC BR 2005 -- 5.4.1 Model of Controlled System -- 5.4.2 Controller Parameters Design and Implementation -- 5.4.3 Experimental Setup and Results -- 5.5 Concluding Remarks -- 6. Field Programmable Analog Array Implementation -- 6.1 The FPAAs Development System -- 6.2 Experimental Results -- 7. Switched Capacitor Integrated Circuit Design -- 7.1 Introduction -- 7.2 Passive and Active Filters -- 7.3 Switched Capacitors Filters -- 7.4 Design of Sampled Data Filters -- 7.4.1 The Impulse Invariance Method -- 7.4.2 The Matched-z Transformation Method -- 7.4.3 Backward Euler Approximation of Derivatives -- 7.4.4 Forward Euler Approximation of Derivatives -- 7.4.5 The Bilinear Transformation Method -- 7.4.6 The Lossless Discrete Integrator Transformation -- 7.5 Switched Capacitor Fundamental Circuits -- 7.5.1 Resistor Realized by Backward Euler Transformation -- 7.6 Circuital Implementation of the Fractional Order Integrator -- 7.7 Switched Capacitors Implementation of Fractional Order Integrator -- 7.8 Results -- 8. Fractional Order Model of IPMC -- 8.1 Fractional Model Identification Introduction -- 8.2 Ionic Polymer Metal Composites (IPMC).

8.3 Actuation Mechanism on IPMCs -- 8.4 State-of-the-Art for IPMC Models -- 8.5 Experimental Setup -- 8.6 Marquardt Algorithm for the Least Squares Estimation -- 8.7 Fractional Models for IPMC Actuators -- 8.7.1 Comparison Between an Integer Model and a Fractional Model of IPMC Actuators -- 8.7.2 Fractional Models for the Electrical and Electromechanical Stages of IPMC Actuators -- Bibliography -- Index.