Complex Conjugate Matrix Equations for Systems and Control
Seiten
2016
|
1st ed. 2017
Springer Verlag, Singapore
978-981-10-0635-7 (ISBN)
Springer Verlag, Singapore
978-981-10-0635-7 (ISBN)
The book is the first book on complex matrix equations including the conjugate of unknown matrices. It observes that there are some significant differences between the real/complex matrix equations and the complex conjugate matrix equations.
The book is the first book on complex matrix equations including the conjugate of unknown matrices. The study of these conjugate matrix equations is motivated by the investigations on stabilization and model reference tracking control for discrete-time antilinear systems, which are a particular kind of complex system with structure constraints. It proposes useful approaches to obtain iterative solutions or explicit solutions for several types of complex conjugate matrix equation. It observes that there are some significant differences between the real/complex matrix equations and the complex conjugate matrix equations. For example, the solvability of a real Sylvester matrix equation can be characterized by matrix similarity; however, the solvability of the con-Sylvester matrix equation in complex conjugate form is related to the concept of con-similarity. In addition, the new concept of conjugate product for complex polynomial matrices is also proposed in order to establish a unifiedapproach for solving a type of complex matrix equation.
The book is the first book on complex matrix equations including the conjugate of unknown matrices. The study of these conjugate matrix equations is motivated by the investigations on stabilization and model reference tracking control for discrete-time antilinear systems, which are a particular kind of complex system with structure constraints. It proposes useful approaches to obtain iterative solutions or explicit solutions for several types of complex conjugate matrix equation. It observes that there are some significant differences between the real/complex matrix equations and the complex conjugate matrix equations. For example, the solvability of a real Sylvester matrix equation can be characterized by matrix similarity; however, the solvability of the con-Sylvester matrix equation in complex conjugate form is related to the concept of con-similarity. In addition, the new concept of conjugate product for complex polynomial matrices is also proposed in order to establish a unifiedapproach for solving a type of complex matrix equation.
Introduction.- Mathematical Prelimilaries.- Iterative Approaches.- Finite Iterative Approaches.- Real Representations Based Approaches.-Polynomial Matrices Based Approaches.- Standard Linear Equations Based Approaches.- Conjugate Products.- Con-Sylvester Sums Based Approaches.
| Erscheinungsdatum | 08.10.2016 |
|---|---|
| Reihe/Serie | Communications and Control Engineering |
| Zusatzinfo | 13 Illustrations, black and white; XVIII, 487 p. 13 illus. |
| Verlagsort | Singapore |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik ► Algebra | |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Technik ► Elektrotechnik / Energietechnik | |
| Schlagworte | Conjugate products • Con-Sylvester matrix equations • Iterative approaches • Kalman-Yakubovich matrix equations • Lyapunov matrix equations • Sylvester matrix equations |
| ISBN-10 | 981-10-0635-0 / 9811006350 |
| ISBN-13 | 978-981-10-0635-7 / 9789811006357 |
| Zustand | Neuware |
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