Fractional Linear Systems And Electrical Circuits
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Fractional Linear Systems and Electrical Circuits
This monograph covers some selected problems of positive and fractional electrical circuits composed of resistors, coils, capacitors and voltage (current) sources. The book consists of 8 chapters, 4 appendices and a list of references. Chapter 1 is devoted to fractional standard and positive continuous-time and discrete-time linear systems without and with delays. In chapter 2 the standard and positive fractional electrical circuits are considered and the fractional electrical circuits in transient states are analyzed. Descriptor linear electrical circuits and their properties are investigated in chapter 3, while chapter 4 is devoted to the stability of fractional standard and positive linear electrical circuits. The reachability, observability and reconstructability of fractional positive electrical circuits and their decoupling zeros are analyzed in chapter 5. The fractional linear electrical circuits with feedbacks are considered in chapter 6. In chapter 7 solutions of minimum energy control for standard and fractional systems with and without bounded inputs is presented. In chapter 8 the fractional continuous-time 2D linear systems described by the Roesser type models are investigated.
Descriptor Systems of Integer and Fractional Orders
This book covers some selected problems of the descriptor integer and fractional order positive continuous-time and discrete-time systems. The book consists of 3 chapters, 4 appendices and the list of references. Chapter 1 is devoted to descriptor integer order continuous-time and discrete-time linear systems. In Chapter 2, descriptor fractional order continuous-time and discrete-time linear systems are considered. Chapter 3 is devoted to the stability of descriptor continuous-time and discrete-time systems of integer and fractional orders. In Appendix A, extensions of the Cayley–Hamilton theorem for descriptor linear systems are given. Some methods for computation of the Drazin inverse are presented in Appendix B. In Appendix C, some basic definitions and theorems on Laplace transforms and Z-transforms are given. Some properties of the nilpotent matrices are given in Appendix D.
Fractional Dynamical Systems: Methods, Algorithms and Applications
This book presents a wide and comprehensive spectrum of issues and problems related to fractional-order dynamical systems. It is meant to be a full-fledge, comprehensive presentation of many aspects related to the broadly perceived fractional-order dynamical systems which constitute an extension of the traditional integer-order-type descriptions. This implies far-reaching consequences, both analytic and algorithmic, because—in general—properties of the traditional integer-order systems cannot be directly extended by a straightforward generalization to fractional-order systems, modeled by fractional-order differential equations involving derivatives of an non-integer order. This can be useful for describing and analyzing, for instance, anomalies in the behavior of various systems, chaotic behavior, etc. The book contains both analytic contributions with state-of-the-art and theoretical foundations, algorithmic implementation of tools and techniques, and—finally—some examples of relevant and successful practical applications.