Linear Algebra and Its Role in Systems Theory
Linear Algebra and Its Role in Systems Theory

Author: Richard A. Brualdi

Publisher:

Published: 1985

Total Pages: 524

ISBN-13:

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This collection of 35 papers, resulting from the 1984 AMS-IMS-SIAM Summer Research Conference, displays the cross-developments between linear algebra (including numerical linear algebra) and systems and control theory. Linear algebraists will see how some beautiful and strong results of control and systems theory can be derived using the concepts of linear algebra; control and systems theorists will find numerically viable algorithms which can be developed for some important control problems. A full appreciation of the material requires an advanced course in linear algebra, a basic course in matrix computation, and a first course in control theory.

Discrete-Time Linear Systems
Discrete-Time Linear Systems

Author: Guoxiang Gu

Publisher: Springer Science & Business Media

Published: 2012-02-14

Total Pages: 459

ISBN-13: 1461422817

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Discrete-Time Linear Systems: Theory and Design with Applications combines system theory and design in order to show the importance of system theory and its role in system design. The book focuses on system theory (including optimal state feedback and optimal state estimation) and system design (with applications to feedback control systems and wireless transceivers, plus system identification and channel estimation).

Max-linear Systems: Theory and Algorithms
Max-linear Systems: Theory and Algorithms

Author: Peter Butkovič

Publisher: Springer Science & Business Media

Published: 2010-08-05

Total Pages: 281

ISBN-13: 1849962995

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Recent years have seen a significant rise of interest in max-linear theory and techniques. Specialised international conferences and seminars or special sessions devoted to max-algebra have been organised. This book aims to provide a first detailed and self-contained account of linear-algebraic aspects of max-algebra for general (that is both irreducible and reducible) matrices. Among the main features of the book is the presentation of the fundamental max-algebraic theory (Chapters 1-4), often scattered in research articles, reports and theses, in one place in a comprehensive and unified form. This presentation is made with all proofs and in full generality (that is for both irreducible and reducible matrices). Another feature is the presence of advanced material (Chapters 5-10), most of which has not appeared in a book before and in many cases has not been published at all. Intended for a wide-ranging readership, this book will be useful for anyone with basic mathematical knowledge (including undergraduate students) who wish to learn fundamental max-algebraic ideas and techniques. It will also be useful for researchers working in tropical geometry or idempotent analysis.

Positive Linear Systems
Positive Linear Systems

Author: Lorenzo Farina

Publisher: John Wiley & Sons

Published: 2011-09-30

Total Pages: 322

ISBN-13: 111803127X

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A complete study on an important class of linear dynamicalsystems-positive linear systems One of the most often-encountered systems in nearly all areas ofscience and technology, positive linear systems is a specific butremarkable and fascinating class. Renowned scientists LorenzoFarina and Sergio Rinaldi introduce readers to the world ofpositive linear systems in their rigorous but highly accessiblebook, rich in applications, examples, and figures. This professional reference is divided into three main parts: Thefirst part contains the definitions and basic properties ofpositive linear systems. The second part, following the theoreticalexposition, reports the main conceptual results, consideringapplicable examples taken from a number of widely used models. Thethird part is devoted to the study of some classes of positivelinear systems of particular relevance in applications (such as theLeontief model, the Leslie model, the Markov chains, thecompartmental systems, and the queueing systems). Readers familiarwith linear algebra and linear systems theory will appreciate theway arguments are treated and presented. Extraordinarily comprehensive, Positive Linear Systemsfeatures: * Applications from a variety of backgrounds including modeling,control engineering, computer science, demography, economics,bioengineering, chemistry, and ecology * References and annotated bibliographies throughout the book * Two appendices concerning linear algebra and linear systemstheory for readers unfamiliar with the mathematics used Farina and Rinaldi make no effort to hide their enthusiasm for thetopics presented, making Positive Linear Systems: Theory andApplications an indispensable resource for researchers andprofessionals in a broad range of fields.

Linear Systems Theory
Linear Systems Theory

Author: Ferenc Szidarovszky

Publisher: Routledge

Published: 2018-05-03

Total Pages: 528

ISBN-13: 1351435205

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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.

Linear Algebra with Applications
Linear Algebra with Applications

Author: Steven J. Leon

Publisher: Prentice Hall

Published: 2006

Total Pages: 0

ISBN-13: 9780131857858

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This thorough and accessible book from one of the leading figures in the field of linear algebra provides readers with both a challenging and broad understanding of linear algebra. The author infuses key concepts with their modern practical applications to offer readers examples of how mathematics is used in the real world. Topics such as linear systems theory, matrix theory, and vector space theory are integrated with real world applications to give a clear understanding of the material and the application of the concepts to solve real world problems. Each chapter contains integrated worked examples and chapter tests. The book stresses the important role geometry and visualization play in understanding linear algebra.For anyone interested in the application of linear algebra theories to solve real world problems.

General Systems Theory: Mathematical Foundations
General Systems Theory: Mathematical Foundations

Author:

Publisher: Academic Press

Published: 1975-03-21

Total Pages: 283

ISBN-13: 008095622X

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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