Research into dynamical systems and control theory implications is a very hot topic J. Willems is well-known researcher and has a very good reputation in nonlinear control theory The book uses a unique behavioral approach for which the authors are well regarded Dynamical systems, controllability, observability and stability are among the many topics of active research that are presented Important, widely applicable modeling techniques are detailed Contains numerous exercises, simulation problems, and examples Will be of interest to applied mathematicians, mechanical and electrical engineers.
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.|Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modem as well as the classical techniques of applied mathematics. This renewal of interest,both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The developmentof new courses is a natural consequenceof a high level of excite ment on the research frontier as newer techniques, such as numerical and symbolic computersystems,dynamicalsystems,and chaos, mix with and reinforce the tradi tional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbookssuitable for use in advancedundergraduate and begin ning graduate courses, and will complement the Applied Mathematical Seiences (AMS) series, which will focus on advanced textbooks and research level mono graphs. Preface Tbe purpose of this preface is twofold. Firstly, to give an informal historical in troduction to the subject area of this book, Systems and Control , and secondly, to explain the philosophy of the approach to this subject taken in this book and to outline the topics that will be covered.|This is a book about modelling, analysis and control of linear time invariant systems. It uses the behavioural approach for which the authors are well regarded. It is a suitable text for senior undergraduates or beginning graduate students in mathematics and engineering and contains numerous exercises, including simulation problems and examples, notably of mechanical systems and electrical circuits.
1 Dynamical Systems.- 2 Systems Defined by Linear Differential Equations.- 3 Time Domain Deillegalscription 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.
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."
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modem as well as the classical techniques of applied mathematics. This renewal of interest,both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The developmentof new courses is a natural consequenceof a high level of excite ment on the research frontier as newer techniques, such as numerical and symbolic computersystems,dynamicalsystems,and chaos, mix with and reinforce the tradi tional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbookssuitable for use in advancedundergraduate and begin ning graduate courses, and will complement the Applied Mathematical Seiences (AMS) series, which will focus on advanced textbooks and research level mono graphs. Preface Tbe purpose of this preface is twofold. Firstly, to give an informal historical in troduction to the subject area of this book, Systems and Control , and secondly, to explain the philosophy of the approach to this subject taken in this book and to outline the topics that will be covered.
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."
Inhaltsverzeichnis
1 Dynamical Systems.- 2 Systems Defined by Linear Differential Equations.- 3 Time Domain Deillegalscription 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.
Klappentext
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modem as well as the classical techniques of applied mathematics. This renewal of interest,both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The developmentof new courses is a natural consequenceof a high level of excite ment on the research frontier as newer techniques, such as numerical and symbolic computersystems,dynamicalsystems,and chaos, mix with and reinforce the tradi tional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbookssuitable for use in advancedundergraduate and begin ning graduate courses, and will complement the Applied Mathematical Seiences (AMS) series, which will focus on advanced textbooks and research level mono graphs. Preface Tbe purpose of this preface is twofold. Firstly, to give an informal historical in troduction to the subject area of this book, Systems and Control , and secondly, to explain the philosophy of the approach to this subject taken in this book and to outline the topics that will be covered.
This is a book about modelling, analysis and control of linear time invariant systems. It uses the behavioural approach for which the authors are well regarded. It is a suitable text for senior undergraduates or beginning graduate students in mathematics and engineering and contains numerous exercises, including simulation problems and examples, notably of mechanical systems and electrical circuits.
