Advances in Dynamics and Control of Fractional Discrete Time Systems: Theories and Applications delves into the cutting-edge developments in the field of fractional discrete time systems. This comprehensive resource bridges the gap between theoretical advancements and practical applications, offering readers a thorough understanding of the dynamics and control mechanisms of these systems. With a blend of rigorous mathematical theory and real-world examples, this book is an essential guide for anyone looking to master the complexities of fractional discrete time systems.
Table of Contents
1. Introduction. Definition and importance of fractional difference systems2. Essential Mathematical Tools. Z-transform, state matrices, and stability theory
3. Fundamentals of Fractional Difference Calculus. Basic concepts and properties
4. Modeling of Fractional Discrete-Time Systems. Methods for building mathematical models
5. Stability of Commensurate Order Systems. Stability criteria and analysis
6. Stability of Incommensurate Order Systems. Advanced methods and analyses
7. Control Methods in Fractional Discrete-Time Systems. Various control techniques
8. Synchronization in Fractional Discrete-Time Systems. Study and mechanisms of synchronization
9. Control of Chaos in Fractional Discrete-Time Systems. Exploring the Control in chaotic Fractional Discrete-Time Systems
10. Applications of Fractional Discrete-Time Systems in Engineering and Science. Practical examples and uses
11. Applications in Epidemic Models. Studying the role of fractional discrete systems in modeling the spread of infectious diseases, stability of disease-free equilibrium, and control strategies
12. Numerical Algorithms. Computational methods for solving fractional equations
13. Design of Robust Control Systems. Strategies for performance improvement
14. Conclusion and Future Perspectives. Summary and future research suggestions
Authors
Adel Ouannas Department of Mathematics, Faculty of Science, Islamic University of Madinah, Saudi Arabia and Department of Mathematics and Computer Science, University of Oum EL-Bouaghi, Oum El Bouaghi, Algeria. Adel Ouannas received his B.S. in Mathematics from Laarbi Ben Mhidi University in 2003, an M.Sc. from the University of Constantine in 2006, and a Ph.D. from the same university in 2015. His research focuses on chaotic and hyperchaotic circuits, fractional-order systems, synchronization properties, chaos-based cryptography, fractional neural networks, and stability of nonlinear systems. Prof. Ouannas has published over 200 journal articles (indexed in Web of Science) and 90 conference papers. Noureddine Djenina Institute of Hygiene and Safety, Mustapha Ben Boulaid University, Fesdis, Batna, Algeria.Noureddine Djenina, born in Tebessa, Algeria, is a researcher in applied mathematics affiliated with the University of Oum El Bouaghi. He also holds a Master's degree in partial differential equations (PDEs) from the University of Tebessa.
Omar Naifar University of Sfax, National School of Engineers of Sfax, Tunisia. Omar Naifar earned his Master's degree in Computer Science in 2010, a Ph.D. in Electrical Engineering in 2015, and the H.D.R. degree in 2021, all from the University of Sfax, Tunisia. He is currently an Associate Professor and a member of the Control and Energy Management Laboratory (CEM-Lab). His research interests include robust nonlinear control, observer design, fault diagnosis, and fractional-order systems. Prof. Naifar is an Associate Editor of the Asian Journal of Control (Wiley). Abdellatif Ben Makhlouf Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Tunisia. Abdellatif Ben Makhlouf received his Bachelor's and Master's degrees in Mathematics and his Ph.D. from the University of Sfax, Tunisia, in 2015. He is currently an Associate Professor of Mathematics at the University of Sfax. His research interests include fractional differential equations, stochastic differential equations, ordinary differential equations, control theory, and stability theory.
