Nonlinear Hybrid Continuous/Discrete-Time Models
The book is mainly about hybrid systems with continuous/discrete-time dynamics. The major part of the book consists of the theory of equations with piece-wise constant argument of generalized type. The systems as well as technique of investigation were in
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Atlantis Studies in Mathematics for Engineering and Science Series Editor: C. K. Chui, Stanford University, USA (ISSN: 1875-7642)
Aims and scope of the series The series ‘Atlantis Studies in Mathematics for Engineering and Science’ (AMES) publishes high quality monographs in applied mathematics, computational mathematics, and statistics that have the potential to make a significant impact on the advancement of engineering and science on the one hand, and economics and commerce on the other. We welcome submission of book proposals and manuscripts from mathematical scientists worldwide who share our vision of mathematics as the engine of progress in the disciplines mentioned above. All books in this series are co-published with World Scientific. For more information on this series and our other book series, please visit our website at: www.atlantis-press.com/publications/books
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Nonlinear Hybrid Continuous/Discrete-Time Models Marat Akhmet Middle East Technical University, Ankara, Turkey
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Atlantis Press 8, square des Bouleaux 75019 Paris, France For information on all Atlantis Press publications, visit our website at: www.atlantis-press.com Copyright This book, or any parts thereof, may not be reproduced for commercial purposes in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system known or to be invented, without prior permission from the Publisher.
Atlantis Studies in Mathematics for Engineering and Science Volume 1: Continued Fractions: Volume 1: Convergence Theory – L. Lorentzen, H. Waadeland Volume 2: Mean Field Theories and Dual Variation – T. Suzuki Volume 3: The Hybrid Grand Unified Theory – V. Lakshmikantham, E. Escultura, S. Leela Volume 4: The Wavelet Transform – R.S. Pathak Volume 5: Theory of Causal Differential Equations – V. Lakshmikantham, S. Leela, Z. Drici Volume 6: The Omega Problem of all Members of the United Nations – E.N. Chukwu Volume 7: Boundary Element Methods with Applications to Nonlinear Problems – G. Chen, J. Zhou
ISBNs Print: E-Book: ISSN:
978-94-91216-02-2 978-94-91216-03-9 1875-7642
c 2011 ATLANTIS PRESS
To my family.
Preface
The dynamical systems theory was shaped by the investigation of stellar and planetary motions. The applications were later extended to isolated mechanisms, electronics and other processes. Analysis was dominated by assumptions of continuity and extension to infinity. At present we face new challenges, such as events with a finite life and models of large dimensions. The processes are interconnected, rather than isolated, and the motions are alternately continuous and discrete. To meet these challenges we need appropriate tools: differential equations with a discontinuous right-hand side, differential equations with impulses and hybrid systems. Hybrid systems are a recent concept in dynamical systems theory and have important applications. Hybrid dynamical systems have not been defined in a precise way yet. Roug
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