Finite Dimensional Linear Systems

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Finite Dimensional Linear Systems

Roger W. Brockett
Finite Dimensional Linear Systems Book PDF

Author : Roger W. Brockett
Publisher : SIAM
Page : 260 pages
File Size : 47,8 Mb
Release : 2015-05-26
Category : Mathematics
ISBN : 9781611973884

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Finite Dimensional Linear Systems by Roger W. Brockett Pdf

Originally published in 1970, Finite Dimensional Linear Systems is a classic textbook that provides a solid foundation for learning about dynamical systems and encourages students to develop a reliable intuition for problem solving. The theory of linear systems has been the bedrock of control theory for 50 years and has served as the springboard for many significant developments, all the while remaining impervious to change. Since linearity lies at the heart of much of the mathematical analysis used in applications, a firm grounding in its central ideas is essential. This book touches upon many of the standard topics in applied mathematics, develops the theory of linear systems in a systematic way, making as much use as possible of vector ideas, and contains a number of nontrivial examples and many exercises.

An Introduction to Infinite-Dimensional Linear Systems Theory

Ruth F. Curtain,Hans Zwart
An Introduction to Infinite Dimensional Linear Systems Theory Book PDF

Author : Ruth F. Curtain,Hans Zwart
Publisher : Springer Science & Business Media
Page : 714 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461242246

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An Introduction to Infinite-Dimensional Linear Systems Theory by Ruth F. Curtain,Hans Zwart Pdf

Infinite dimensional systems is now an established area of research. Given the recent trend in systems theory and in applications towards a synthesis of time- and frequency-domain methods, there is a need for an introductory text which treats both state-space and frequency-domain aspects in an integrated fashion. The authors' primary aim is to write an introductory textbook for a course on infinite dimensional linear systems. An important consideration by the authors is that their book should be accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Consequently, all the mathematical background is summarized in an extensive appendix. For the majority of students, this would be their only acquaintance with infinite dimensional systems.

Stability of Finite and Infinite Dimensional Systems

Michael I. Gil'
Stability of Finite and Infinite Dimensional Systems Book PDF

Author : Michael I. Gil'
Publisher : Springer Science & Business Media
Page : 386 pages
File Size : 55,8 Mb
Release : 1998-09-30
Category : Mathematics
ISBN : 0792382218

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Stability of Finite and Infinite Dimensional Systems by Michael I. Gil' Pdf

The aim of Stability of Finite and Infinite Dimensional Systems is to provide new tools for specialists in control system theory, stability theory of ordinary and partial differential equations, and differential-delay equations. Stability of Finite and Infinite Dimensional Systems is the first book that gives a systematic exposition of the approach to stability analysis which is based on estimates for matrix-valued and operator-valued functions, allowing us to investigate various classes of finite and infinite dimensional systems from the unified viewpoint. This book contains solutions to the problems connected with the Aizerman and generalized Aizerman conjectures and presents fundamental results by A. Yu. Levin for the stability of nonautonomous systems having variable real characteristic roots. Stability of Finite and Infinite Dimensional Systems is intended not only for specialists in stability theory, but for anyone interested in various applications who has had at least a first-year graduate-level course in analysis.

Mathematical Control Theory

Eduardo D. Sontag
Mathematical Control Theory Book PDF

Author : Eduardo D. Sontag
Publisher : Springer Science & Business Media
Page : 543 pages
File Size : 54,9 Mb
Release : 2013-11-21
Category : Mathematics
ISBN : 9781461205777

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Mathematical Control Theory by Eduardo D. Sontag Pdf

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.

Linear System Theory

Frank M. Callier,Charles A. Desoer
Linear System Theory Book PDF

Author : Frank M. Callier,Charles A. Desoer
Publisher : Springer Science & Business Media
Page : 524 pages
File Size : 53,9 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461209577

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Linear System Theory by Frank M. Callier,Charles A. Desoer Pdf

This book is the result of our teaching over the years an undergraduate course on Linear Optimal Systems to applied mathematicians and a first-year graduate course on Linear Systems to engineers. The contents of the book bear the strong influence of the great advances in the field and of its enormous literature. However, we made no attempt to have a complete coverage. Our motivation was to write a book on linear systems that covers finite dimensional linear systems, always keeping in mind the main purpose of engineering and applied science, which is to analyze, design, and improve the performance of phy sical systems. Hence we discuss the effect of small nonlinearities, and of perturbations of feedback. It is our on the data; we face robustness issues and discuss the properties hope that the book will be a useful reference for a first-year graduate student. We assume that a typical reader with an engineering background will have gone through the conventional undergraduate single-input single-output linear systems course; an elementary course in control is not indispensable but may be useful for motivation. For readers from a mathematical curriculum we require only familiarity with techniques of linear algebra and of ordinary differential equations.

State Space and Input-Output Linear Systems

David F. Delchamps
State Space and Input Output Linear Systems Book PDF

Author : David F. Delchamps
Publisher : Springer Science & Business Media
Page : 431 pages
File Size : 42,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461238164

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State Space and Input-Output Linear Systems by David F. Delchamps Pdf

It is difficult for me to forget the mild sense of betrayal I felt some ten years ago when I discovered, with considerable dismay, that my two favorite books on linear system theory - Desoer's Notes for a Second Course on Linear Systems and Brockett's Finite Dimensional Linear Systems - were both out of print. Since that time, of course, linear system theory has undergone a transformation of the sort which always attends the maturation of a theory whose range of applicability is expanding in a fashion governed by technological developments and by the rate at which such advances become a part of engineering practice. The growth of the field has inspired the publication of some excellent books; the encyclopedic treatises by Kailath and Chen, in particular, come immediately to mind. Nonetheless, I was inspired to write this book primarily by my practical needs as a teacher and researcher in the field. For the past five years, I have taught a one semester first year gradu ate level linear system theory course in the School of Electrical Engineering at Cornell. The members of the class have always come from a variety of departments and backgrounds, and con sequently have entered the class with levels of preparation ranging from first year calculus and a taste of transform theory on the one extreme to senior level real analysis and abstract algebra on the other.

Finite-Dimensional Linear Algebra

Mark S. Gockenbach
Finite Dimensional Linear Algebra Book PDF

Author : Mark S. Gockenbach
Publisher : CRC Press
Page : 674 pages
File Size : 42,7 Mb
Release : 2011-06-15
Category : Mathematics
ISBN : 9781439815649

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Finite-Dimensional Linear Algebra by Mark S. Gockenbach Pdf

Linear algebra forms the basis for much of modern mathematics—theoretical, applied, and computational. Finite-Dimensional Linear Algebra provides a solid foundation for the study of advanced mathematics and discusses applications of linear algebra to such diverse areas as combinatorics, differential equations, optimization, and approximation. The author begins with an overview of the essential themes of the book: linear equations, best approximation, and diagonalization. He then takes students through an axiomatic development of vector spaces, linear operators, eigenvalues, norms, and inner products. In addition to discussing the special properties of symmetric matrices, he covers the Jordan canonical form, an important theoretical tool, and the singular value decomposition, a powerful tool for computation. The final chapters present introductions to numerical linear algebra and analysis in vector spaces, including a brief introduction to functional analysis (infinite-dimensional linear algebra). Drawing on material from the author’s own course, this textbook gives students a strong theoretical understanding of linear algebra. It offers many illustrations of how linear algebra is used throughout mathematics.

Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces

Birgit Jacob,Hans J. Zwart
Linear Port Hamiltonian Systems on Infinite dimensional Spaces Book PDF

Author : Birgit Jacob,Hans J. Zwart
Publisher : Springer Science & Business Media
Page : 221 pages
File Size : 52,6 Mb
Release : 2012-06-13
Category : Science
ISBN : 9783034803991

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Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces by Birgit Jacob,Hans J. Zwart Pdf

This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the first textbook on infinite-dimensional port-Hamiltonian systems. An abstract functional analytical approach is combined with the physical approach to Hamiltonian systems. This combined approach leads to easily verifiable conditions for well-posedness and stability. The book is accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Moreover, the theory is illustrated by many worked-out examples.

Elementary Feedback Stabilization of the Linear Reaction-Convection-Diffusion Equation and the Wave Equation

Weijiu Liu
Elementary Feedback Stabilization of the Linear Reaction Convection Diffusion Equation and the Wave Equation Book PDF

Author : Weijiu Liu
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 41,8 Mb
Release : 2009-12-01
Category : Mathematics
ISBN : 9783642046131

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Elementary Feedback Stabilization of the Linear Reaction-Convection-Diffusion Equation and the Wave Equation by Weijiu Liu Pdf

Unlike abstract approaches to advanced control theory, this volume presents key concepts through concrete examples. Once the basic fundamentals are established, readers can apply them to solve other control problems of partial differential equations.

Finite-dimensional Linear Analysis

I. M. Glazman
Finite dimensional Linear Analysis Book PDF

Author : I. M. Glazman
Publisher : Courier Corporation
Page : 548 pages
File Size : 55,6 Mb
Release : 2006-01-01
Category : Mathematics
ISBN : 9780486453323

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Finite-dimensional Linear Analysis by I. M. Glazman Pdf

A sequence of 2,400 propositions and problems features only hints. Suitable for advanced undergraduates and graduate students, this unique approach encourages students to work out their own proofs. 1974 edition.

System Theory of Continuous Time Finite Dimensional Dynamical Systems

Yasumichi Hasegawa
System Theory of Continuous Time Finite Dimensional Dynamical Systems Book PDF

Author : Yasumichi Hasegawa
Publisher : Springer Nature
Page : 221 pages
File Size : 50,8 Mb
Release : 2019-09-26
Category : Technology & Engineering
ISBN : 9783030304805

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System Theory of Continuous Time Finite Dimensional Dynamical Systems by Yasumichi Hasegawa Pdf

This book discusses the realization and control problems of finite-dimensional dynamical systems which contain linear and nonlinear systems. The author focuses on algebraic methods for the discussion of control problems of linear and non-linear dynamical systems. The book contains detailed examples to showcase the effectiveness of the presented method. The target audience comprises primarily research experts in the field of control theory, but the book may also be beneficial for graduate students alike.

Iterative Methods for Sparse Linear Systems

Yousef Saad
Iterative Methods for Sparse Linear Systems Book PDF

Author : Yousef Saad
Publisher : SIAM
Page : 537 pages
File Size : 40,6 Mb
Release : 2003-04-01
Category : Mathematics
ISBN : 9780898715347

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Iterative Methods for Sparse Linear Systems by Yousef Saad Pdf

Mathematics of Computing -- General.

The Theory of Linear Systems

J. E. Rubio
The Theory of Linear Systems Book PDF

Author : J. E. Rubio
Publisher : Academic Press
Page : 344 pages
File Size : 52,7 Mb
Release : 2013-10-22
Category : Technology & Engineering
ISBN : 9781483219875

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The Theory of Linear Systems by J. E. Rubio Pdf

The Theory of Linear Systems presents the state-phase analysis of linear systems. This book deals with the transform theory of linear systems, which had most of its success when applied to time-invariant systems. Organized into nine chapters, this book begins with an overview of the development of some properties of simple differential systems that are mostly of a nonalgebraic nature. This text then presents a brief treatment of vector spaces, matrices, transformations, norms, and inner products. Other chapters deal with the inductive process used to define dynamical systems. This book discusses as well the existence and uniqueness theorem for the solutions of a homogeneous linear differential system. The final chapter deals with the abstract concept of a dynamical system and derives properties of these systems. This book is a valuable resource for advanced graduate students in areas such as economics and bioengineering. Engineers engaged in systems design will also find this book useful.

Finite Dimensional Vector Spaces. (AM-7), Volume 7

Paul R. Halmos
Finite Dimensional Vector Spaces AM 7 Volume 7 Book PDF

Author : Paul R. Halmos
Publisher : Princeton University Press
Page : 196 pages
File Size : 50,5 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882236

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Finite Dimensional Vector Spaces. (AM-7), Volume 7 by Paul R. Halmos Pdf

As a newly minted Ph.D., Paul Halmos came to the Institute for Advanced Study in 1938--even though he did not have a fellowship--to study among the many giants of mathematics who had recently joined the faculty. He eventually became John von Neumann's research assistant, and it was one of von Neumann's inspiring lectures that spurred Halmos to write Finite Dimensional Vector Spaces. The book brought him instant fame as an expositor of mathematics. Finite Dimensional Vector Spaces combines algebra and geometry to discuss the three-dimensional area where vectors can be plotted. The book broke ground as the first formal introduction to linear algebra, a branch of modern mathematics that studies vectors and vector spaces. The book continues to exert its influence sixty years after publication, as linear algebra is now widely used, not only in mathematics but also in the natural and social sciences, for studying such subjects as weather problems, traffic flow, electronic circuits, and population genetics. In 1983 Halmos received the coveted Steele Prize for exposition from the American Mathematical Society for "his many graduate texts in mathematics dealing with finite dimensional vector spaces, measure theory, ergodic theory, and Hilbert space."

Theory of Stabilization for Linear Boundary Control Systems

Takao Nambu
Theory of Stabilization for Linear Boundary Control Systems Book PDF

Author : Takao Nambu
Publisher : CRC Press
Page : 285 pages
File Size : 47,9 Mb
Release : 2017-03-03
Category : Mathematics
ISBN : 9781498758482

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Theory of Stabilization for Linear Boundary Control Systems by Takao Nambu Pdf

This book presents a unified algebraic approach to stabilization problems of linear boundary control systems with no assumption on finite-dimensional approximations to the original systems, such as the existence of the associated Riesz basis. A new proof of the stabilization result for linear systems of finite dimension is also presented, leading to an explicit design of the feedback scheme. The problem of output stabilization is discussed, and some interesting results are developed when the observability or the controllability conditions are not satisfied.