Mathematical systems theory / Diederich Hinrichsen, Anthony J. Pritchard.

Format:

Book

Author/Creator:

Hinrichsen, Diederich, 1939-

Contributor:

Pritchard, A. J.

Anne and Joseph Trachtman Memorial Book Fund.

Series:

Texts in applied mathematics ; 48.

Texts in applied mathematics ; 48

Language:

English

Subjects (All):

System theory--Mathematics.

System analysis--Mathematics.

System analysis.

Mathematics.

System theory.

Physical Description:

volumes : illustrations ; 24 cm.

Place of Publication:

Berlin ; New York : Springer, c2005.

Summary:

This book presents the mathematical foundations of systems and control theory in a self-contained, comprehensive, detailed and mathematically rigorous way. The first volume is devoted to the state space analysis of dynamical systems with special emphasis on problems of uncertainty, whereas the second volume will be devoted to problems of control and measurement. The work combines features of a detailed introductory textbook with that of a reference source.

The first chapter of this volume is of an illustrative and motivational character. It presents a catalogue of dynamic models from six areas of application. The development of mathematical systems theory starts in Chapter 2 with an introduction to the state space description of dynamical systems. This introduction is followed by three substantial chapters on stability theory, perturbation theory and the analysis of uncertain systems. Special features are: a comprehensive treatment of Liapunov's stability theory, a detailed exposition of algebraic stability criteria, a presentation of classical perturbation theory for polynomials and matrices, a systematic introduction to [mu]-analysis, a development of spectral value sets as tools for robustness analysis, an account of stability radii as robustness measures for various perturbation classes, a study of the transient behaviour of linear systems.

Throughout the book there are many examples and figures illustrating the text which help to bring out the intuitive ideas behind the mathematical constructions. The book should be accessible to mathematics students after two years of study and also to engineering students with a good mathematical background. In this volume the reader is gradually brought to the frontiers of research in stability and robustness analysis. It will, therefore, be of value for researchers in systems theory as well as mathematicians and engineers who wish to learn about the mathematical foundations of systems and control.

Contents:

1. Modelling, state space analysis, stability and robustness

Notes:

Includes bibliographical references (pages 763-788) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Anne and Joseph Trachtman Memorial Book Fund.

ISBN:

3540441255

OCLC:

57579826

Publisher Number:

9783540441250