Singular Perturbation Analysis of Discrete Control Systems
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1154 D.S. Naidu A.K. Rao
Singular Perturbation Analysis of Discrete Control Systems
Spri nger-Verlag Berlin Heidelberg New York Tokyo
Authors Desineni S. Naidu Guidance and Control Division, NASA Langley Research Center Hampton, VA 23665, USA Ayalasomayajula K. Rao Department of Electrical Engineering, J. N. Technical University Hyderabad, AP. 500028, India
Mathematics Subject Classification (1980): 34E 15, 39A 10, 93C55 ISBN 3-540-15981-9 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-15981-9 Springer-Verlag New York Heidelberg Berlin Tokyo
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© by Springer-Verlag Berlin Heidelberg 1985 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2146/3140-543210
Dedicated to
Mother and Father (DSN)
and
Mother (AKR)
ACKNOWLEDGEMENTS The authors would like to express their deep gratitude to Professor P. K. Rajagopalan of Indian Institute of Technology Kharagpur for introducing the subject to the authors and for his inspiration. One of the authors (DSN) had a gainful experience under the influence of the works of Professor P. V. Kokotovic of University of Illinois, Ubana-Champaign, Professor P. Sannuti of Rutgers University, Piscataway, and Professor R. E. O'Malley, Jr., of Rennselaer Polytechnic Institute, Troy. The permission given by Taylor & Francis Ltd. (International Journal of control) and John Wiley & Sons (Optimal control: Applications & Methods) to reproduce some of the material published by the authors is acknowledged. Thanks are due to National Research council (NRC) which offered a Senior Research Associateship to one of the authors (DSN) tenable at Flight Dynamics and Control Division, NASA Langley Research Center, Hampton, where the monograph took the final shape. Special mention should be made about Dr. Douglas B. Price who took keen interest and the entire staff who did a marvellous job in the final preparation of the monograph. Finally, the authors wish to record their high appreciation of their families who made several cheerful sacrifices during the entire period of their research work.
PREFACE The dynamics of many control systems is described by higher order differential equations. However, the behaviour is governed by a few dominant parameters, a relatively minor role being played by the remaining parameters such as small time constants, masses, moments of inertia, inductances and capacitances. The presence of these "parasitic" parameters is often the source for the increased order and the "stiffness" of the system. The "curse" of this dimensionality coupled with stiffness causes formidable computational difficulties for the ana
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