Author : Diederich Hinrichsen
Publisher : Springer Science & Business Media
Page : 818 pages
File Size : 17,41 MB
Release : 2011-08-03
Category : Mathematics
ISBN : 3540441255
This book presents the mathematical foundations of systems theory in a self-contained, comprehensive, detailed and mathematically rigorous way. It is devoted to the analysis of dynamical systems and combines features of a detailed introductory textbook with that of a reference source. The book contains many examples and figures illustrating the text which help to bring out the intuitive ideas behind the mathematical constructions.
Author : J.C. Willems
Publisher : Springer Science & Business Media
Page : 446 pages
File Size : 48,30 MB
Release : 2013-11-11
Category : Mathematics
ISBN : 1475729537
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.
Author : Christiaan Heij
Publisher : Springer Science & Business Media
Page : 169 pages
File Size : 32,30 MB
Release : 2006-12-18
Category : Science
ISBN : 3764375493
This book provides an introduction to the theory of linear systems and control for students in business mathematics, econometrics, computer science, and engineering; the focus is on discrete time systems. The subjects treated are among the central topics of deterministic linear system theory: controllability, observability, realization theory, stability and stabilization by feedback, LQ-optimal control theory. Kalman filtering and LQC-control of stochastic systems are also discussed, as are modeling, time series analysis and model specification, along with model validation.
Author : Joachim Rosenthal
Publisher : Springer Science & Business Media
Page : 528 pages
File Size : 25,78 MB
Release : 2003-09-02
Category : Science
ISBN : 9780387403199
This volume contains survey and research articles by some of the leading researchers in mathematical systems theory - a vibrant research area in its own right. Many authors have taken special care that their articles are self-contained and accessible also to non-specialists.
Author : Eduardo D. Sontag
Publisher : Springer Science & Business Media
Page : 543 pages
File Size : 16,39 MB
Release : 2013-11-21
Category : Mathematics
ISBN : 1461205778
Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. The minimal mathematical background required is a working knowledge of linear algebra and differential equations. The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.
Author :
Publisher : Academic Press
Page : 283 pages
File Size : 41,64 MB
Release : 1975-03-21
Category : Technology & Engineering
ISBN : 008095622X
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
Author : Jan Haluska
Publisher : CRC Press
Page : 430 pages
File Size : 21,75 MB
Release : 2003-12-19
Category : Mathematics
ISBN : 9780824747145
The Mathematical Theory of Tone Systems patterns a unified theory defining the tone system in functional terms based on the principles and forms of uncertainty theory. This title uses geometrical nets and other measures to study all classes of used and theoretical tone systems, from Pythagorean tuning to superparticular pentatonics. Hundreds of examples of past and prevalent tone systems are featured. Topics include Fuzziness and Sonance, Wavelets and Nonspecificity, Pitch Granulation and Ambiguity, Equal Temperaments, Mean Tone Systems. Well Tempered Systems, Ptolemy Systems, and more. Appendices include extended lists of tone systems and a catalogue of historical organs with subsemitones.
Author : Athanasios C. Antoulas
Publisher : Springer Science & Business Media
Page : 589 pages
File Size : 37,71 MB
Release : 2013-04-17
Category : Technology & Engineering
ISBN : 3662085461
Over the past three decades R.E. Kalman has been one of the most influential personalities in system and control theory. His ideas have been instrumental in a variety of areas. This is a Festschrift honoring his 60th birthday. It contains contributions from leading researchers in the field giving an account of the profound influence of his ideas in a number of areas of active research in system and control theory. For example, since their introduction by Kalman in the early 60's, the concepts of controllability and observability of dynamical systems with inputs, have been the corner stone of the great majority of investigations in the field.
Author : V.N. Afanasiev
Publisher : Springer Science & Business Media
Page : 676 pages
File Size : 19,87 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 940172203X
Give, and it shall be given unto you. ST. LUKE, VI, 38. The book is based on several courses of lectures on control theory and appli cations which were delivered by the authors for a number of years at Moscow Electronics and Mathematics University. The book, originally written in Rus sian, was first published by Vysshaya Shkola (Higher School) Publishing House in Moscow in 1989. In preparing a new edition of the book we planned to make only minor changes in the text. However, we soon realized that we like many scholars working in control theory had learned many new things and had had many new insights into control theory and its applications since the book was first published. Therefore, we rewrote the book especially for the English edition. So, this is substantially a new book with many new topics. The book consists of an introduction and four parts. Part One deals with the fundamentals of modern stability theory: general results concerning stability and instability, sufficient conditions for the stability of linear systems, methods for determining the stability or instability of systems of various type, theorems on stability under random disturbances.
Author : Jerzy Zabczyk
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 37,6 MB
Release : 2008
Category : Language Arts & Disciplines
ISBN : 9780817647322
In a mathematically precise manner, this book presents a unified introduction to deterministic control theory. It includes material on the realization of both linear and nonlinear systems, impulsive control, and positive linear systems.
