Introduction to Mathematical Systems Theory
A Behavioral Approach
Published on 1. November 1997
Book
Hardback
XXX, 424 pages
978-0-387-98266-3 (ISBN)
Description
Using the behavioural approach to mathematical modelling, this book views a system as a dynamical relation between manifest and latent variables. The emphasis is on dynamical systems that are represented by systems of linear constant coefficients. The first part analyses the structure of the set of trajectories generated by such dynamical systems, and derives the conditions for two systems of differential equations to be equivalent in the sense that they define the same behaviour. In addition the memory structure of the system is analysed through state space models. The second part of the book is devoted to a number of important system properties, notably controllability, observability, and stability. In the third part, control problems are considered, in particular stabilisation and pole placement questions. Suitable for advanced undergraduate or beginning graduate students in mathematics and engineering, this text contains numerous exercises, including simulation problems, and examples, notably of mechanical systems and electrical circuits.
Reviews / Votes
From the reviews: INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL "The present book is a major original contribution to the literature and is of high quality. The most original chapters are the 'strongly behavioural' Chapters 1-6 and the historical preface. The introduction is carefully written and each chapter ends with a precise recapitulation of what has been done. It is well organized, technically well written, philosophically nice, and contains a wealth of examples and exercises. It is also well self-contained for its audience!scientific honesty dictates to congratulate the authors and to recommend this book as a textbook to a large public of systems and control students, and especially for those having already followed a first course on linear systems."More details
Series
Edition
1997
Language
English
Place of publication
NY
United States
Target group
College/higher education
Professional and scholarly
Graduate
Illustrations
89 black & white illustrations
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Thickness: 26 mm
Weight
760 gr
ISBN-13
978-0-387-98266-3 (9780387982663)
DOI
10.1007/978-1-4757-2953-5
Schweitzer Classification
Other editions
New editions
Jan Willem Polderman | Jan C. Willems
Introduction to Mathematical Systems Theory
A Behavioral Approach
Book
02/2013
2nd Edition
Springer
€50.24
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Book
03/2013
Springer
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Content
1 Dynamical Systems.- 2 Systems Defined by Linear Differential Equations.- 3 Time Domain Description of Linear Systems.- 4 State Space Models.- 5 Controllability and Observability.- 6 Elimination of Latent Variables and State Space Representations.- 7 Stability Theory.- 8 Time- and Frequency-Domain Characteristics of Linear Time-Invariant Systems.- 9 Pole Placement by State Feedback.- 10 Observers and Dynamic Compensators.- A Simulation Exercises.- A.1 Stabilization of a Cart.- A.2 Temperature Control of a Container.- A.3 Autonomous Dynamics of Coupled Masses.- A.4 Satellite Dynamics.- A.4.1 Motivation.- A.4.2 Mathematical modeling.- A.4.3 Equilibrium Analysis.- A.4.4 Linearization.- A.4.5 Analysis of the model.- A.4.6 Simulation.- A.5 Dynamics of a Motorbike.- A.6 Stabilization of a Double Pendulum.- A.6.1 Modeling.- A.6.2 Linearization.- A.6.3 Analysis.- A.6.4 Stabilization.- A.7 Notes and References.- B Background Material.- B.1 Polynomial Matrices.- B.2 Partial Fraction Expansion.- B.3 Fourier and Laplace Transforms.- B.3.1 Fourier transform.- B.3.2 Laplace transform.- B.4 Notes and References.- B.5 Exercises.- Notation.- References.