Complex Conjugate Matrix Equations for Systems and Control

1. Auflage 2017
ISBN: 978-981-10-0635-7
Verlag: Springer Nature Singapore

Buch, Englisch, 487 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 8808 g

Reihe: Communications and Control Engineering

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.

Zielgruppe

Research

Autoren/Hrsg.

Zhang, Ying

Wu, Ai-Guo

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Regelungstechnik
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie

Inhaltsverzeichnis

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.