Introduction to Mathematical Systems Theory: A Behavioral Approach

2. nd Auflage 2007
ISBN: 978-0-387-35763-8
Verlag: Springer

Buch, Englisch, Band 26, 445 Seiten, GB, Format (B × H): 155 mm x 235 mm

Reihe: Texts in Applied Mathematics

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.

Zielgruppe

Graduates, senior undergraduates

Autoren/Hrsg.

Polderman, Jan Willem

Willems, Jan C.

Fachgebiete

• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Naturwissenschaften Chemie Chemie Allgemein Chemometrik, Chemoinformatik

Inhaltsverzeichnis

Preface.- Dynamical Systems.- Introduction.- Models.- The universum and the behavior.- Behavioral equations.- Latent variables.- Dynamical systems.- The basic 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.