The Mathematics Of Networks Of Linear Systems

Author : Paul A. Fuhrmann,Uwe Helmke
Publisher : Unknown
Page : 128 pages
File Size : 41,6 Mb
Release : 2015
Category : Electronic
ISBN : 3319166476

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The Mathematics of Networks of Linear Systems by Paul A. Fuhrmann,Uwe Helmke Pdf

This book provides the mathematical foundations of networks of linear control systems, developed from an algebraic systems theory perspective. This includes a thorough treatment of questions of controllability, observability, realization theory, as well as feedback control and observer theory. The potential of networks for linear systems in controlling large-scale networks of interconnected dynamical systems could provide insight into a diversity of scientific and technological disciplines. The scope of the book is quite extensive, ranging from introductory material to advanced topics of current research, making it a suitable reference for graduate students and researchers in the field of networks of linear systems. Part I can be used as the basis for a first course in algebraic system theory, while Part II serves for a second, advanced, course on linear systems. Finally, Part III, which is largely independent of the previous parts, is ideally suited for advanced research seminars aimed at preparing graduate students for independent research. "Mathematics of Networks of Linear Systems" contains a large number of exercises and examples throughout the text making it suitable for graduate courses in the area.

Author : Paul A. Fuhrmann,Uwe Helmke
Publisher : Springer
Page : 662 pages
File Size : 44,5 Mb
Release : 2015-05-26
Category : Mathematics
ISBN : 9783319166469

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The Mathematics of Networks of Linear Systems by Paul A. Fuhrmann,Uwe Helmke Pdf

This book provides the mathematical foundations of networks of linear control systems, developed from an algebraic systems theory perspective. This includes a thorough treatment of questions of controllability, observability, realization theory, as well as feedback control and observer theory. The potential of networks for linear systems in controlling large-scale networks of interconnected dynamical systems could provide insight into a diversity of scientific and technological disciplines. The scope of the book is quite extensive, ranging from introductory material to advanced topics of current research, making it a suitable reference for graduate students and researchers in the field of networks of linear systems. Part I can be used as the basis for a first course in Algebraic System Theory, while Part II serves for a second, advanced, course on linear systems. Finally, Part III, which is largely independent of the previous parts, is ideally suited for advanced research seminars aimed at preparing graduate students for independent research. “Mathematics of Networks of Linear Systems” contains a large number of exercises and examples throughout the text making it suitable for graduate courses in the area.

Author : Ferenc Szidarovszky
Publisher : Routledge
Page : 528 pages
File Size : 42,5 Mb
Release : 2018-05-03
Category : Mathematics
ISBN : 9781351435208

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Linear Systems Theory by Ferenc Szidarovszky Pdf

This second edition comprehensively presents important tools of linear systems theory, including differential and difference equations, Laplace and Z transforms, and more. Linear Systems Theory discusses: Nonlinear and linear systems in the state space form and through the transfer function method Stability, including marginal stability, asymptotical stability, global asymptotical stability, uniform stability, uniform exponential stability, and BIBO stability Controllability Observability Canonical forms System realizations and minimal realizations, including state space approach and transfer function realizations System design Kalman filters Nonnegative systems Adaptive control Neural networks The book focuses mainly on applications in electrical engineering, but it provides examples for most branches of engineering, economics, and social sciences. What's New in the Second Edition? Case studies drawn mainly from electrical and mechanical engineering applications, replacing many of the longer case studies Expanded explanations of both linear and nonlinear systems as well as new problem sets at the end of each chapter Illustrative examples in all the chapters An introduction and analysis of new stability concepts An expanded chapter on neural networks, analyzing advances that have occurred in that field since the first edition Although more mainstream than its predecessor, this revision maintains the rigorous mathematical approach of the first edition, providing fast, efficient development of the material. Linear Systems Theory enables its reader to develop his or her capabilities for modeling dynamic phenomena, examining their properties, and applying them to real-life situations.

Author : Ferenc Szidarovszky,A. Terry Bahill
Publisher : CRC Press
Page : 530 pages
File Size : 44,7 Mb
Release : 1997-11-25
Category : Technology & Engineering
ISBN : 0849316871

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Linear Systems Theory, Second Edition by Ferenc Szidarovszky,A. Terry Bahill Pdf

This second edition comprehensively presents important tools of linear systems theory, including differential and difference equations, Laplace and Z transforms, and more. Linear Systems Theory discusses: Nonlinear and linear systems in the state space form and through the transfer function method Stability, including marginal stability, asymptotical stability, global asymptotical stability, uniform stability, uniform exponential stability, and BIBO stability Controllability Observability Canonical forms System realizations and minimal realizations, including state space approach and transfer function realizations System design Kalman filters Nonnegative systems Adaptive control Neural networks The book focuses mainly on applications in electrical engineering, but it provides examples for most branches of engineering, economics, and social sciences. What's New in the Second Edition? Case studies drawn mainly from electrical and mechanical engineering applications, replacing many of the longer case studies Expanded explanations of both linear and nonlinear systems as well as new problem sets at the end of each chapter Illustrative examples in all the chapters An introduction and analysis of new stability concepts An expanded chapter on neural networks, analyzing advances that have occurred in that field since the first edition Although more mainstream than its predecessor, this revision maintains the rigorous mathematical approach of the first edition, providing fast, efficient development of the material. Linear Systems Theory enables its reader to develop his or her capabilities for modeling dynamic phenomena, examining their properties, and applying them to real-life situations.

Author : Srinivasan Keshav
Publisher : Addison-Wesley
Page : 496 pages
File Size : 54,6 Mb
Release : 2012-04-20
Category : Computers
ISBN : 9780132826136

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Mathematical Foundations of Computer Networking by Srinivasan Keshav Pdf

“To design future networks that are worthy of society’s trust, we must put the ‘discipline’ of computer networking on a much stronger foundation. This book rises above the considerable minutiae of today’s networking technologies to emphasize the long-standing mathematical underpinnings of the field.” –Professor Jennifer Rexford, Department of Computer Science, Princeton University “This book is exactly the one I have been waiting for the last couple of years. Recently, I decided most students were already very familiar with the way the net works but were not being taught the fundamentals–the math. This book contains the knowledge for people who will create and understand future communications systems." –Professor Jon Crowcroft, The Computer Laboratory, University of Cambridge The Essential Mathematical Principles Required to Design, Implement, or Evaluate Advanced Computer Networks Students, researchers, and professionals in computer networking require a firm conceptual understanding of its foundations. Mathematical Foundations of Computer Networking provides an intuitive yet rigorous introduction to these essential mathematical principles and techniques. Assuming a basic grasp of calculus, this book offers sufficient detail to serve as the only reference many readers will need. Each concept is described in four ways: intuitively; using appropriate mathematical notation; with a numerical example carefully chosen for its relevance to networking; and with a numerical exercise for the reader. The first part of the text presents basic concepts, and the second part introduces four theories in a progression that has been designed to gradually deepen readers’ understanding. Within each part, chapters are as self-contained as possible. The first part covers probability; statistics; linear algebra; optimization; and signals, systems, and transforms. Topics range from Bayesian networks to hypothesis testing, and eigenvalue computation to Fourier transforms. These preliminary chapters establish a basis for the four theories covered in the second part of the book: queueing theory, game theory, control theory, and information theory. The second part also demonstrates how mathematical concepts can be applied to issues such as contention for limited resources, and the optimization of network responsiveness, stability, and throughput.

Author : Kai-Sheng Lu
Publisher : World Scientific
Page : 319 pages
File Size : 43,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814412438

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Rational Function Systems and Electrical Networks with Multi-parameters by Kai-Sheng Lu Pdf

To overcome the problems of system theory and network theory over real field, this book uses matrices over the field F ( z ) of rational functions in multi-parameters describing coefficient matrices of systems and networks and makes systems and network description over F ( z ) and researches their structural properties: reducible condition of a class of matrices over F ( z ) and their characteristic polynomial; type-1 matrix and two basic properties; variable replacement conditions for independent parameters; structural controllability and observability of linear systems over F ( z ); separability, reducibility, controllability, observability and structural conditions of networks over F ( z ), and so on. This book involves three subjects: systems, networks and matrices over F ( z ), which is an achievement of interdisciplinary research. Sample Chapter(s). Chapter 1: Introduction (166 KB). Contents: Introduction; Matrices Over Field F ( z ) of Rational Functions in Multi-Parameters; Controllability and Observability of Linear Systems Over F ( z ); Electrical Networks Over F ( z ); Further Thought. Readership: For researchers, graduate students, and engineers in the field of electrical engineering, electronics, automation and applied mathematics (matrix theory).

Author : W. K. Chen
Publisher : World Scientific
Page : 0 pages
File Size : 48,9 Mb
Release : 1990
Category : Computers
ISBN : 9789971506841

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Linear Networks and Systems by W. K. Chen Pdf

This two-volume introductory text on modern network and system theory establishes a firm analytic foundation for the analysis, design and optimization of a wide variety of passive and active circuits. Volume 1 is devoted to the fundamentals and Volume 2 to Fourier analysis and state equations. Its prerequisites are basic calculus, dc and ac networks, matrix algebra, and some familiarity with linear differential equations. The objective of the book is to select and feature theories and concepts of fundamental importance that are amendable to a broad range of applications. A special feature of the book is that it bridges the gap between theory and practice, with abundant examples showing how theory solves problems. Recognizing that computers are common tools in modern engineering, canned computer programs are developed throughout the text, both in the time domain and the frequency domain. In addition to the usual materials in a linear networks and systems book, advanced topics on functions of a matrix that are closely related to the solution of the state equation are included. The reader will find the study of this material rewarding.

Author : P.A. Fuhrmann
Publisher : Springer
Page : 938 pages
File Size : 55,8 Mb
Release : 1984-03
Category : Language Arts & Disciplines
ISBN : UCAL:B4406426

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Mathematical Theory of Networks and Systems by P.A. Fuhrmann Pdf

Author : Wai-Kai Chen
Publisher : Elsevier
Page : 559 pages
File Size : 44,8 Mb
Release : 2014-11-28
Category : Mathematics
ISBN : 9781483164151

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Applied Graph Theory by Wai-Kai Chen Pdf

Applied Graph Theory: Graphs and Electrical Networks, Second Revised Edition provides a concise discussion of the fundamentals of graph and its application to the electrical network theory. The book emphasizes the mathematical precision of the concepts and principles involved. The text first covers the basic theory of graph, and then proceeds to tackling in the next three chapters the various applications of graph to electrical network theory. These chapters also discuss the foundations of electrical network theory; directed-graph solutions of linear algebraic equations; and topological analysis of linear systems. Next, the book covers trees and their generation. Chapter 6 deals with the realizability of directed graphs with prescribed degrees, while Chapter 7 talks about state equations of networks. The book will be of great use to researchers of network topology, linear systems, and circuitries.

Author : Roger W. Brockett
Publisher : SIAM
Page : 260 pages
File Size : 48,9 Mb
Release : 2015-05-26
Category : Mathematics
ISBN : 9781611973877

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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.

Author : Daniel Alpay,Mihaela B. Vajiac
Publisher : Springer
Page : 316 pages
File Size : 54,8 Mb
Release : 2019-08-08
Category : Mathematics
ISBN : 9783030184841

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Linear Systems, Signal Processing and Hypercomplex Analysis by Daniel Alpay,Mihaela B. Vajiac Pdf

This volume includes contributions originating from a conference held at Chapman University during November 14-19, 2017. It presents original research by experts in signal processing, linear systems, operator theory, complex and hypercomplex analysis and related topics.

Author : Oswaldo Luiz do Valle Costa,Marcelo D. Fragoso,Marcos G. Todorov
Publisher : Springer Science & Business Media
Page : 295 pages
File Size : 52,9 Mb
Release : 2012-12-18
Category : Mathematics
ISBN : 9783642341007

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Continuous-Time Markov Jump Linear Systems by Oswaldo Luiz do Valle Costa,Marcelo D. Fragoso,Marcos G. Todorov Pdf

It has been widely recognized nowadays the importance of introducing mathematical models that take into account possible sudden changes in the dynamical behavior of a high-integrity systems or a safety-critical system. Such systems can be found in aircraft control, nuclear power stations, robotic manipulator systems, integrated communication networks and large-scale flexible structures for space stations, and are inherently vulnerable to abrupt changes in their structures caused by component or interconnection failures. In this regard, a particularly interesting class of models is the so-called Markov jump linear systems (MJLS), which have been used in numerous applications including robotics, economics and wireless communication. Combining probability and operator theory, the present volume provides a unified and rigorous treatment of recent results in control theory of continuous-time MJLS. This unique approach is of great interest to experts working in the field of linear systems with Markovian jump parameters or in stochastic control. The volume focuses on one of the few cases of stochastic control problems with an actual explicit solution and offers material well-suited to coursework, introducing students to an interesting and active research area. The book is addressed to researchers working in control and signal processing engineering. Prerequisites include a solid background in classical linear control theory, basic familiarity with continuous-time Markov chains and probability theory, and some elementary knowledge of operator theory. ​

Author : Hermann Kremer
Publisher : Artech House Publishers
Page : 216 pages
File Size : 46,8 Mb
Release : 1987
Category : Mathematics
ISBN : UOM:39015012754670

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Numerical Analysis of Linear Networks and Systems by Hermann Kremer Pdf

Author : Christopher I. Byrnes,Biswa N. Datta,Clyde F. Martin
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 54,6 Mb
Release : 2013-12-11
Category : Science
ISBN : 9781461241201

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Systems and Control in the Twenty-First Century by Christopher I. Byrnes,Biswa N. Datta,Clyde F. Martin Pdf

The mathematical theory of networks and systems has a long, and rich history, with antecedents in circuit synthesis and the analysis, design and synthesis of actuators, sensors and active elements in both electrical and mechanical systems. Fundamental paradigms such as the state-space real ization of an input/output system, or the use of feedback to prescribe the behavior of a closed-loop system have proved to be as resilient to change as were the practitioners who used them. This volume celebrates the resiliency to change of the fundamental con cepts underlying the mathematical theory of networks and systems. The articles presented here are among those presented as plenary addresses, invited addresses and minisymposia presented at the 12th International Symposium on the Mathematical Theory of Networks and Systems, held in St. Louis, Missouri from June 24 - 28, 1996. Incorporating models and methods drawn from biology, computing, materials science and math ematics, these articles have been written by leading researchers who are on the vanguard of the development of systems, control and estimation for the next century, as evidenced by the application of new methodologies in distributed parameter systems, linear nonlinear systems and stochastic sys tems for solving problems in areas such as aircraft design, circuit simulation, imaging, speech synthesis and visionics.

Author : Anne Greenbaum
Publisher : SIAM
Page : 235 pages
File Size : 48,9 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 1611970938

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Iterative Methods for Solving Linear Systems by Anne Greenbaum Pdf

Much recent research has concentrated on the efficient solution of large sparse or structured linear systems using iterative methods. A language loaded with acronyms for a thousand different algorithms has developed, and it is often difficult even for specialists to identify the basic principles involved. Here is a book that focuses on the analysis of iterative methods. The author includes the most useful algorithms from a practical point of view and discusses the mathematical principles behind their derivation and analysis. Several questions are emphasized throughout: Does the method converge? If so, how fast? Is it optimal, among a certain class? If not, can it be shown to be near-optimal? The answers are presented clearly, when they are known, and remaining important open questions are laid out for further study. Greenbaum includes important material on the effect of rounding errors on iterative methods that has not appeared in other books on this subject. Additional important topics include a discussion of the open problem of finding a provably near-optimal short recurrence for non-Hermitian linear systems; the relation of matrix properties such as the field of values and the pseudospectrum to the convergence rate of iterative methods; comparison theorems for preconditioners and discussion of optimal preconditioners of specified forms; introductory material on the analysis of incomplete Cholesky, multigrid, and domain decomposition preconditioners, using the diffusion equation and the neutron transport equation as example problems. A small set of recommended algorithms and implementations is included.