Monografia prof. Tadeusza Kaczorka i dr. Łukasza Sajewskiego
Realization Problem for Positive and Fractional Systems
By
Tadeusz Kaczorek and Lukasz Sajewski
Printing House of Bialystok University of Technology, Bialystok, Poland, 2013
Hardcover, 665 pages, ISSN 0867-096X
Professor Tadeusz Kaczorek is IEEE Fellow and well-known expert, author of 25 books related to control theory. After his last successful book “Selected Problems in Fractional Systems Theory” [1], he and coauthor Lukasz Sajewski now present a new monograph devoted to positive and fractional systems. Although the fractional calculus has a long history going back into XVII centaury, its applications has re-attracted considerable interest only in the past three/four decades and include areas of science and engineering such as: acoustic wave propagation in inhomogeneous materials, diffusive transport, fluid flow, dynamics of earthquakes, optics, geology, viscoelastic materials, bio-sciences, medicine, economics, probability and statistics, astrophysics, chemical engineering, physics, electromagnetic waves, etc [2]. Also, in signal processing, automatic control theory and systems a growing interest is observed [3]. The presented book contributes to this developments presenting applications in control theory and systems.
The book consists of the following eight chapters and five appendices:
Chapter I: “Realization problem of 1D standard linear systems”
Chapter II: “Realization problem of 1D positive regular linear systems”
Chapter III: “Realization problem of 1D positive regular linear systems with delays”
Chapter IV: “Positive stable realization problem for 1D regular linear systems”
Chapter V: “Positive realization problem of 1D descriptor linear systems”
Chapter VI: “Positive realization problem for 1D regular fractional linear systems”
Chapter VII: “Positive realization problem for 1D descriptor fractional linear systems”
Chapter VIII: “Positive realization problem for 2D continuous-discrete linear systems”
Appendix A: “Elementary operations on matrices, matrix equations with nonnegative solutions and shuffle algorithm”
Appendix B: “Positive regular continuous-time and discrete-time systems”
Appendix C: “Fractional linear systems”
Appendix D: “Minimal and cyclic realizations and structure stability of normal transfer matrices”
Appendix E: “Positive 2D continuous-discrete linear systems and its solution”.
The monograph is written with strong mathematical rigorous, however Authors have made significant effort to unify symbols and approach throughout the book. Also, numerous examples added in each chapter can be very helpful for better understanding and for self-study.
The book is addressed to graduate and PhD-students as well as researches from the field of automatic control and systems theory. It can also be recommended to undergraduate students in electrical, electronics, mechatronics and computer engineering departments.
REFERENCES
[1] T. Kaczorek, “ Selected Problems in Fractional Systems Theory”, Springer Verlag, 2011.
[2] D. Cafagna, “Fractional Calculus: A Mathematical Tool from the Past for Present Engineers”, IEEE Ind. Electron. Mag., vol. 1, no. 2, pp. 35-40, 2007.
[2] M. S. Tavazoei, “From Traditional to Fractional PI Control. A Key for Generalization”, IEEE Ind. Electron. Mag., vol. 6, no. 3, pp. 41-51, 2012.
Marian P. Kazmierkowski
Wydz. IV Nauk Technicznych PAN
