Jan Willem Polderman, Jan C. Willems

Introduction to Mathematical Systems Theory: A Behavioral Approach

• Gebundenes Buch

Produktbeschreibung

This is a book about modelling, analysis and control of linear time- invariant systems. The book uses what is called the behavioral approach towards mathematical modelling. Thus a system is viewed as a dynamical relation between manifest and latent variables. The emphasis is on dynamical systems that are represented by systems of linear constant coefficients. In the first part of the book the structure of the set of trajectories that such dynamical systems generate is analyzed. Conditions are obtained for two systems of differential equations to be equivalent in the sense that they define the same behavior. It is further shown that the trajectories of such linear differential systems can be partitioned in free inputs and bound outputs. In addition the memory structure of the system is analyzed through state space models. The second part of the book is devoted to a number of important system properties, notably controllability, observability, and stability. An essential feature of using the behavioral approach is that it allows these and similar concepts to be introduced in a representation-free manner. In the third part control problems are considered, more specifically stabilization and pole placement questions. This text is suitable for advanced undergraduate or beginning graduate students in mathematics and engineering. It contains numerous exercises, including simulation problems, and examples, notably of mechanical systems and electrical circuits.

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Produktdetails

• Texts in Applied Mathematics Vol.26
• Verlag: Springer, Berlin
• Artikelnr. des Verlages: 11608172
• 2nd ed.
• Seitenzahl: 455
• Erscheinungstermin: Oktober 2007
• Englisch
• Abmessung: 235mm x 155mm
• Gewicht: 756g
• ISBN-13: 9780387357638
• ISBN-10: 0387357637
• Artikelnr.: 20856000

Autorenporträt

Jan Willem Polderman, University of Twente, Enschede, The Netherlands / Jan C. Willems, University of Leuven, Belgium

Inhaltsangabe

Preface.- Dynamical Systems.- Introduction.- Models.- The universum and the behavior.- Behavioral equations.- Latent variables.- Dynamical systems.- Thebasic concept.- Latent variables in dynamical systems.- Linearity and time-invariance.- Dynamical behavioral equations.- Recapitulation .- Notes and references.- Exercises.- Systems defined by Linear Differential Equations.- Notation.

Rezensionen

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."