Introduction to Mathematical Systems Theory: A Behavioral Approach: 26 - Brossura

Polderman, Jan Willem; Willems, Jan C.

Brossura

ISBN 10: 1475729553 ISBN 13: 9781475729559

Casa editrice: Springer Nature, 2013

Riassunto

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.

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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."

Contenuti:

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.

Su questa edizione

• Editore: Springer Nature
• Data di pubblicazione: 2013
• ISBN 10: 1475729553
• ISBN 13: 9781475729559
• Rilegatura: Copertina flessibile
• Numero di pagine: 424