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Complex Conjugate Matrix Equations for Systems and Control

  • Book
  • © 2017

Overview

Authors:
  1. Ai-Guo Wu

    1. University Town of Shenzhen, Harbin Institute of Technology, Shenzhen, Shenzhen, China

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  2. Ying Zhang

    1. University Town of Shenzhen, Harbin Institute of Technology, Shenzhen, Shenzhen, China

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    You can also search for this author in PubMed   Google Scholar

  • Offers iterative solutions and explicit solutions for some complex conjugate matrix equations
  • Observes the differences between the real/complex matrix equations and complex conjugate matrix equations
  • Provides a full picture of this field for researchers and introduces some new concepts, such as conjugate products and con-­Sylvester-­sum as well
  • Includes supplementary material: sn.pub/extras

Part of the book series: Communications and Control Engineering (CCE)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Introduction

    • Ai-Guo Wu, Ying Zhang
    Pages 1-34

  3. Mathematical Preliminaries

    • Ai-Guo Wu, Ying Zhang
    Pages 35-93

  4. Iterative Solutions

    1. Front Matter

      Pages 95-95
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    2. Smith-Type Iterative Approaches

      • Ai-Guo Wu, Ying Zhang
      Pages 97-118

    3. Hierarchical-Update-Based Iterative Approaches

      • Ai-Guo Wu, Ying Zhang
      Pages 119-162

    4. Finite Iterative Approaches

      • Ai-Guo Wu, Ying Zhang
      Pages 163-221

  5. Explicit Solutions

    1. Front Matter

      Pages 223-223
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    2. Real-Representation-Based Approaches

      • Ai-Guo Wu, Ying Zhang
      Pages 225-274

    3. Polynomial-Matrix-Based Approaches

      • Ai-Guo Wu, Ying Zhang
      Pages 275-334

    4. Unilateral-Equation-Based Approaches

      • Ai-Guo Wu, Ying Zhang
      Pages 335-354

    5. Conjugate Products

      • Ai-Guo Wu, Ying Zhang
      Pages 355-387

    6. Con-Sylvester-Sum-Based Approaches

      • Ai-Guo Wu, Ying Zhang
      Pages 389-402

  6. Applications in Systems and Control

    1. Front Matter

      Pages 403-403
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    2. Stability for Antilinear Systems

      • Ai-Guo Wu, Ying Zhang
      Pages 405-438

    3. Feedback Design for Antilinear Systems

      • Ai-Guo Wu, Ying Zhang
      Pages 439-470

  7. Back Matter

    Pages 471-487
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Keywords

About this book

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.

Reviews

“The book is well organized and presents the most important notions of iterative solutions, explicit solutions and applications in systems and control. The book is suitable for senior undergraduate and graduate students as well as practical engineers, scientist and researchers interested in iterative, explicit solutions and of applications in systems and control.” (Seenith Sivasundaram, zbMATH 1371.15003, 2017)

Authors and Affiliations

  • University Town of Shenzhen, Harbin Institute of Technology, Shenzhen, Shenzhen, China

    Ai-Guo Wu, Ying Zhang

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