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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.
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.
"The book is a very interesting mathematical study of descriptor (singular) systems of classic-integer and fractional orders. ... The book is very nicely written and may be suggested for researchers interested in mathematical background of control systems theory." ( Krzysztof Galkowski, zbMATH 1492.93006, 2022)