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© 2017

Complex Conjugate Matrix Equations for Systems and Control

Book

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

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Ai-Guo Wu, Ying Zhang
    Pages 1-34
  3. Ai-Guo Wu, Ying Zhang
    Pages 35-93
  4. Iterative Solutions

    1. Front Matter
      Pages 95-95
    2. Ai-Guo Wu, Ying Zhang
      Pages 97-118
    3. Ai-Guo Wu, Ying Zhang
      Pages 119-162
    4. Ai-Guo Wu, Ying Zhang
      Pages 163-221
  5. Explicit Solutions

    1. Front Matter
      Pages 223-223
    2. Ai-Guo Wu, Ying Zhang
      Pages 225-274
    3. Ai-Guo Wu, Ying Zhang
      Pages 275-334
    4. Ai-Guo Wu, Ying Zhang
      Pages 335-354
    5. Ai-Guo Wu, Ying Zhang
      Pages 355-387
    6. Ai-Guo Wu, Ying Zhang
      Pages 389-402
  6. Applications in Systems and Control

    1. Front Matter
      Pages 403-403
    2. Ai-Guo Wu, Ying Zhang
      Pages 405-438
    3. Ai-Guo Wu, Ying Zhang
      Pages 439-470
  7. Back Matter
    Pages 471-487

About this book

Introduction

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 unified approach for solving a type of complex matrix equation.

Keywords

Con-Sylvester matrix equations Conjugate products Iterative approaches Kalman-Yakubovich matrix equations Lyapunov matrix equations Sylvester matrix equations

Authors and affiliations

  1. 1.University Town of ShenzhenHarbin Institute of Technology, ShenzhenShenzhenChina
  2. 2.University Town of ShenzhenHarbin Institute of Technology, ShenzhenShenzhenChina

Bibliographic information

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Electronics
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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)