Analysis, Modeling and Stability of Fractional Order Differential Systems 2 : The Infinite State Approach.
Trigeassou, Jean-Claude.
Analysis, Modeling and Stability of Fractional Order Differential Systems 2 : The Infinite State Approach. - 1st ed. - 1 online resource (352 pages)
Intro -- Table of Contents -- Foreword -- Preface -- PART 1: Initialization, State Observation and Control -- 1 Initialization of Fractional Order Systems -- 1.1. Introduction -- 1.2. Initialization of an integer order differential system -- 1.3. Initialization of a fractional differential equation -- 1.4. Initialization of a fractional differential system -- 1.5. Some initialization examples -- 2 Observability and Controllability of FDEs/FDSs -- 2.1. Introduction -- 2.2. A survey of classical approaches to the observability and controllability of fractional differential systems -- 2.3. Pseudo-observability and pseudo-controllability of an FDS -- 2.4. Observability and controllability of the distributed state -- 2.5. Conclusion -- 3 Improved Initialization of Fractional Order Systems -- 3.1. Introduction -- 3.2. Initialization: problem statement -- 3.3. Initialization with a fractional observer -- 3.4. Improved initialization -- A.3. Appendix -- 4 State Control of Fractional Differential Systems -- 4.1. Introduction -- 4.2. Pseudo-state control of an FDS -- 4.3. State control of the elementary FDE -- 4.4. State control of an FDS -- 4.5. Conclusion -- 5 Fractional Model-based Control of the Diffusive RC Line -- 5.1. Introduction -- 5.2. Identification of the RC line using a fractional model -- 5.3. Reset of the RC line -- PART 2: Stability of Fractional Differential Equations and Systems -- 6 Stability of Linear FDEs Using the Nyquist Criterion -- 6.1. Introduction -- 6.2. Simulation and stability of fractional differential equations -- 6.3. Stability of ordinary differential equations -- 6.4. Stability analysis of FDEs -- 6.5. Stability analysis of ODEs with time delays -- 6.6. Stability analysis of FDEs with time delays -- 7 Fractional Energy -- 7.1. Introduction -- 7.2. Pseudo-energy stored in a fractional integrator. 7.3. Energy stored and dissipated in a fractional integrator -- 7.4. Closed-loop and open-loop fractional energies -- 8 Lyapunov Stability of Commensurate Order Fractional Systems -- 8.1. Introduction -- 8.2. Lyapunov stability of a one-derivative FDE -- 8.3. Lyapunov stability of an N-derivative FDE -- 8.4. Lyapunov stability of a two-derivative commensurate order FDE -- 8.5. Lyapunov stability of an N-derivative FDE (N > -- 2) -- A.8. Appendix -- 9 Lyapunov Stability of Non-commensurate Order Fractional Systems -- 9.1. Introduction -- 9.2. Stored energy, dissipation and energy balance in fractional electrical devices -- 9.3. The usual series RLC circuit -- 9.4. The series RLC* fractional circuit -- 9.5. The series RLL*C* circuit -- 9.6. The series RL*C* fractional circuit -- 9.7. Stability of a commensurate order FDE: energy balance approach -- 9.8. Stability of a commensurate order FDE: physical interpretation of the usual approach -- A.9. Appendix -- 10 An Introduction to the Lyapunov Stability of Nonlinear Fractional Order Systems -- 10.1. Introduction -- 10.2. Indirect Lyapunov method -- 10.3. Lyapunov direct method -- 10.4. The Van der Pol oscillator -- 10.5. Analysis of local stability -- 10.6. Large signal analysis -- References -- Index -- End User License Agreement.
9781119686842
Fractional calculus.
Electronic books.
QA314 / .T754 2020
Analysis, Modeling and Stability of Fractional Order Differential Systems 2 : The Infinite State Approach. - 1st ed. - 1 online resource (352 pages)
Intro -- Table of Contents -- Foreword -- Preface -- PART 1: Initialization, State Observation and Control -- 1 Initialization of Fractional Order Systems -- 1.1. Introduction -- 1.2. Initialization of an integer order differential system -- 1.3. Initialization of a fractional differential equation -- 1.4. Initialization of a fractional differential system -- 1.5. Some initialization examples -- 2 Observability and Controllability of FDEs/FDSs -- 2.1. Introduction -- 2.2. A survey of classical approaches to the observability and controllability of fractional differential systems -- 2.3. Pseudo-observability and pseudo-controllability of an FDS -- 2.4. Observability and controllability of the distributed state -- 2.5. Conclusion -- 3 Improved Initialization of Fractional Order Systems -- 3.1. Introduction -- 3.2. Initialization: problem statement -- 3.3. Initialization with a fractional observer -- 3.4. Improved initialization -- A.3. Appendix -- 4 State Control of Fractional Differential Systems -- 4.1. Introduction -- 4.2. Pseudo-state control of an FDS -- 4.3. State control of the elementary FDE -- 4.4. State control of an FDS -- 4.5. Conclusion -- 5 Fractional Model-based Control of the Diffusive RC Line -- 5.1. Introduction -- 5.2. Identification of the RC line using a fractional model -- 5.3. Reset of the RC line -- PART 2: Stability of Fractional Differential Equations and Systems -- 6 Stability of Linear FDEs Using the Nyquist Criterion -- 6.1. Introduction -- 6.2. Simulation and stability of fractional differential equations -- 6.3. Stability of ordinary differential equations -- 6.4. Stability analysis of FDEs -- 6.5. Stability analysis of ODEs with time delays -- 6.6. Stability analysis of FDEs with time delays -- 7 Fractional Energy -- 7.1. Introduction -- 7.2. Pseudo-energy stored in a fractional integrator. 7.3. Energy stored and dissipated in a fractional integrator -- 7.4. Closed-loop and open-loop fractional energies -- 8 Lyapunov Stability of Commensurate Order Fractional Systems -- 8.1. Introduction -- 8.2. Lyapunov stability of a one-derivative FDE -- 8.3. Lyapunov stability of an N-derivative FDE -- 8.4. Lyapunov stability of a two-derivative commensurate order FDE -- 8.5. Lyapunov stability of an N-derivative FDE (N > -- 2) -- A.8. Appendix -- 9 Lyapunov Stability of Non-commensurate Order Fractional Systems -- 9.1. Introduction -- 9.2. Stored energy, dissipation and energy balance in fractional electrical devices -- 9.3. The usual series RLC circuit -- 9.4. The series RLC* fractional circuit -- 9.5. The series RLL*C* circuit -- 9.6. The series RL*C* fractional circuit -- 9.7. Stability of a commensurate order FDE: energy balance approach -- 9.8. Stability of a commensurate order FDE: physical interpretation of the usual approach -- A.9. Appendix -- 10 An Introduction to the Lyapunov Stability of Nonlinear Fractional Order Systems -- 10.1. Introduction -- 10.2. Indirect Lyapunov method -- 10.3. Lyapunov direct method -- 10.4. The Van der Pol oscillator -- 10.5. Analysis of local stability -- 10.6. Large signal analysis -- References -- Index -- End User License Agreement.
9781119686842
Fractional calculus.
Electronic books.
QA314 / .T754 2020