Linear, Time-varying Approximations to Nonlinear Dynamical Systems w
Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild conditions on the system nonlinearities, setting it apart fro
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María Tomás-Rodríguez and Stephen P. Banks
Linear, Time-varying Approximations to Nonlinear Dynamical Systems with Applications in Control and Optimization
ABC
Series Advisory Board P. Fleming, P. Kokotovic, A.B. Kurzhanski, H. Kwakernaak, A. Rantzer, J.N. Tsitsiklis
Authors Dr. María Tomás-Rodríguez
Prof. Stephen P. Banks
City University London School of Engineering & Mathematical Sciences Northampton Square London United Kingdom E-mail: [email protected]
University of Sheffield Dept. Automatic Control & Systems Engineering Mappin Street Sheffield United Kingdom E-mail: s.banks@sheffield.ac.uk
ISBN 978-1-84996-100-4
e-ISBN 978-1-84996-101-1
DOI 10.1007/978-1-84996-101-1 Lecture Notes in Control and Information Sciences
ISSN 0170-8643
Library of Congress Control Number: 2009942768 c 2010
Springer-Verlag Berlin Heidelberg
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To my parents and brother, (M T-R). To David and Xu, (S P B).
Preface
This book is the culmination of several years’ research on nonlinear systems. In contrast to the case of linear systems, where a coherent and well-defined theory has existed for many years (indeed, in many respects, we may regard linear systems theory as ‘complete’), nonlinear systems theory has tended to be a set of disparate results on fairly specific kinds of systems. Of course, there are coherent theories of nonlinear systems using differential and/or algebraic geometric methods, but, in many cases, these have very strong conditions attached which are not satisfied in general. In an attempt to build a theory which has great generality we have been led to consider systems with the structure x˙ = A(x;u)x+B(x;u)u (possibly also with a measurement equation). This appears to be quite restrictive, but, as we shall see, almost every system can be put in this form, so that the theory is, in fact, almost completely general. We shall show that systems of this form can be approximated arbitrarily closely
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