State Space Consistency and Differentiability
By investigating the properties of the natural state, this book presents an analysis of input-output systems with regard to the mathematical concept of state. The state of a system condenses the effects of past inputs to the system in a useful manner. Th
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Demetrios Serakos
State Space Consistency and Differentiability
123
SpringerBriefs in Optimization Series Editors Panos M. Pardalos János D. Pintér Stephen M. Robinson Tamás Terlaky My T. Thai
SpringerBriefs in Optimization showcases algorithmic and theoretical techniques, case studies, and applications within the broad-based field of optimization. Manuscripts related to the ever-growing applications of optimization in applied mathematics, engineering, medicine, economics, and other applied sciences are encouraged.
More information about this series at http://www.springer.com/series/8918
Demetrios Serakos
State Space Consistency and Differentiability
123
Demetrios Serakos Dahlgren, VA, USA
ISSN 2190-8354 ISSN 2191-575X (electronic) SpringerBriefs in Optimization ISBN 978-3-319-14468-9 ISBN 978-3-319-14469-6 (eBook) DOI 10.1007/978-3-319-14469-6 Library of Congress Control Number: 2014958663 Mathematics Subject Classification (2010): 93B28; 47N70; 47N20 Springer Cham Heidelberg New York Dordrecht London © Demetrios Serakos 2014 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 Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)
Memory of Georgia (Pantelopoulos) and Demetrios Serakos
Foreword
This book presents an analysis of input–output systems with regard to the mathematical concept of “state.” The state of a system condenses, in a usable way, the effects of past inputs to the system. This book is the result of a theoretical examination of the state concept and the conditions under which state assumptions are valid. The results developed in this book are useful aids for understanding proper modeling of physical systems, including the development of guidance and control algorithms, and in developing simulations. An earlier version of this book appeared as a Naval Surface Warfare Center, Dahlgren Division technical report.1 The author is indebted to Professor William L. Root
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