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Nonlinear Control Under Nonconstant Delays

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by Nikolaos Bekiaris-Liberis and Miroslav Krstic


2013 / xii + 302 pages / Hardcover / ISBN: 978-1-611973-17-4 / List Price $105.50 / SIAM Member Price $73.85 / Order Code DC25

Keywords: control theory, delay systems, nonlinear control, Lyapunov functions, distributed parameter systems


The authors have developed a methodology for control of nonlinear systems in the presence of long delays, with large and rapid variation in the actuation or sensing path, or in the presence of long delays affecting the internal state of a system. In addition to control synthesis, they introduce tools to quantify the performance and the robustness properties of the designs provided in the book.

The book is based on the concept of predictor feedback and infinite-dimensional backstepping transformation for linear systems and the authors guide the reader from the basic ideas of the concept—with constant delays only on the input—all the way through to nonlinear systems with state-dependent delays on the input as well as on system states.

Readers will find the book useful because the authors provide elegant and systematic treatments of long-standing problems in delay systems, such as systems with state-dependent delays that arise in many applications. In addition, the authors give all control designs by explicit formulae, making the book especially useful for engineers who have faced delay-related challenges and are concerned with actual implementations and they accompany all control designs with Lyapunov-based analysis for establishing stability and performance guarantees.

This book is intended for researchers working on control of delay systems, including engineers, mathematicians, and students.

About the Authors
Nikolaos Bekiaris-Liberis received his PhD from University of California, San Diego, and is currently a postdoctoral scholar at University of California, Berkeley. His research interests are in delay systems, distributed parameter systems, and nonlinear control.

Miroslav Krstic is the Alspach endowed professor, founding director of the Cymer Center for Control Systems and Dynamics, and Associate Vice Chancellor for Research at University of California, San Diego. He is a Fellow of IEEE and IFAC; a recipient of the PECASE, NSF Career, and ONR Young Investigator Awards; and the winner of Axelby and Schuck Paper Prizes. He has held distinguished visiting professorships at UC Berkeley and with the Royal Academy of Engineering, UK. He has coauthored nine books, including Boundary Control of PDEs: A Course on Backstepping Designs (SIAM, 2008).

ISBN: 9781611973174

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