Approximate and Noisy Realization of Linear Representation Systems
Let the set of output’s values Y be a linear space over the field \(\boldsymbol{R}\) . In the reference [Matsuo and Hasegawa, 2003], linear representation systems were presented with the following main theorem. The main theorem says that for any causal in
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Yasumichi Hasegawa
Approximate and Noisy Realization of Discrete-Time Dynamical Systems
ABC
Series Advisory Board F. Allgöwer, P. Fleming, P. Kokotovic, A.B. Kurzhanski, H. Kwakernaak, A. Rantzer, J.N. Tsitsiklis
Author Prof. Yasumichi Hasegawa Department of Electronics Gifu University Gifu, 501-1193 Japan E-Mail: [email protected]
ISBN 978-3-540-79433-2
e-ISBN 978-3-540-79434-9
DOI 10.1007/978-3-540-79434-9 Lecture Notes in Control and Information Sciences
ISSN 0170-8643
Library of Congress Control Number: 2008925333 c 2008
Springer-Verlag Berlin Heidelberg
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Preface
This monograph deals with approximation and noise cancellation of dynamical systems which include linear and nonlinear input/output relations. It will be of special interest to researchers, engineers and graduate students who have specialized in filtering theory and system theory. From noisy or noiseless data, reduction will be made. A new method which reduces noise or models information will be proposed. Using this method will allow model description to be treated as noise reduction or model reduction. As proof of the efficacy, this monograph provides new results and their extensions which can also be applied to nonlinear dynamical systems. To present the effectiveness of our method, many actual examples of noise and model information reduction will also be provided. Using the analysis of state space approach, the model reduction problem may have become a major theme of technology after 1966 for emphasizing efficiency in the fields of control, economy, numerical analysis, and others. Noise reduction problems in the analysis of noisy dynamical systems may have become a major theme of technology after 1974 for emphasizing efficiency in control. However, the subjects of these researches have been mainly concentrated in linear systems. In common model reduction of linear systems in use today, a singular value decomposition of a Hankel matrix is used to find a reduced order model. However, the existence of the conditions of the reduced order model are derived without evaluation
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