Finite Iterative Approaches
In Chap. 3 , Smith-type iterative algorithms are presented for con-Kalman-Yakubovich matrix equations. In Chap. 4 , iterative approaches have been established for some more complicated complex conjugate matrix equations.
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Ai-Guo Wu Ying Zhang
Complex Conjugate Matrix Equations for Systems and Control
Communications and Control Engineering Series editors Alberto Isidori, Roma, Italy Jan H. van Schuppen, Amsterdam, The Netherlands Eduardo D. Sontag, Piscataway, USA Miroslav Krstic, La Jolla, USA
More information about this series at http://www.springer.com/series/61
Ai-Guo Wu Ying Zhang •
Complex Conjugate Matrix Equations for Systems and Control
123
Ai-Guo Wu Harbin Institute of Technology, Shenzhen University Town of Shenzhen Shenzhen China
Ying Zhang Harbin Institute of Technology, Shenzhen University Town of Shenzhen Shenzhen China
ISSN 0178-5354 ISSN 2197-7119 (electronic) Communications and Control Engineering ISBN 978-981-10-0635-7 ISBN 978-981-10-0637-1 (eBook) DOI 10.1007/978-981-10-0637-1 Library of Congress Control Number: 2016942040 Mathematics Subject Classification (2010): 15A06, 11Cxx © Springer Science+Business Media Singapore 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer Science+Business Media Singapore Pte Ltd.
To our supervisor, Prof. Guang-Ren Duan To Hong-Mei, and Yi-Tian To Rui, and Qi-Yu
(Ai-Guo Wu)
(Ying Zhang)
Preface
Theory of matrix equations is an important branch of mathematics, and has broad applications in many engineering fields, such as control theory, information theory, and signal processing. Specifically, algebraic Lyapunov matrix equations play vital roles in stability analysis for linear systems, and coupled Lyapunov matrix equations appear in the analysis for Markovian jump linear systems; algebraic Riccati equations are encountered in optimal control. Due to these reasons, matrix equations are extensively investigated by many scholars from various fields, and the content on matrix equations has been very rich. Matrix equations are often covered in some books on linear algebra, matrix analysis, and numerical analysis. We l
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