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Matrix diagonal stability and the related diagonal type Liapunov functions possess properties that make them attractive and very useful for applications. This new book addresses the matrix-stability concept and its applications to the analysis and design of several types of dynamical systems, both discrete-time and continuous-time.

The comprehensive presentation begins with an introductory chapter surveying applied examples from diverse fields, i.e., robust stability analysis, asynchronous iterative computation, neural networks and variable structure dynamical systems. The next few chapters develop the theory and includes a unified presentation of results in the area of matrix-diagonal stability and D-stability. The remaining chapters examine the various applications in greater detail. Both classical and new results are discussed, and the overall treatment is self-contained, only requiring linear algebra, difference equations and differential equations.

Topics and Features:

Diverse applications presented with minimum of technical prerequisites
Unified presentation of results on discrete-time and continuous-time diagonal and D-stability
Extensive guide to current literature and discussion of open problems
Asynchronous iterative methods
Stability and stabilization
Neural networks, circuits and systems

"Matrix Diagonal Stability in Systems and Computation" provides an essential reference for new methods and analysis related to dynamical systems described by linear and nonlinear ordinary differential equations and difference equations. Researchers, professionals and graduates in applied math, control engineering, stability of dynamical systems, scientific computation and computer science will find the book a successful guide to current results and developments. ... Read more

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From the reviews: "Do you know M.Padberg's Linear Optimization and Extensions? […] Now here is the continuation of it, discussing the solutions of all its exercises and with detailed analysis of the applications mentioned. Tell your students about it. […] For those who strive for good exercises and case studies for LP this is an excellent volume." Acta Scientiarum Mathematicarum

Customer Reviews (2)

Computational and Mathematical Excellence
For nearly 30 years, Padberg has been a leader in computational integer programming and in combinatorial optimization theory.

In practice, Padberg has helped to design and implement "branch-and-cut" methods for finding exact optimal solutions to large traveling salesman problems, and this approach is a method of choice for finding approximately optimal solutions to tough industrial problems.The book provides the mathematical and computational background for understanding branch-and-cut; the established mathematical texts by Nemhauser and Wolsey and by Schrijver are less detailed and more condensed, and omit numerical issues.The treatment of modern simplex algorithms for linear programming---updating LU factorizations and using column- and constraint-generation and -purging---is excellent, and a large bibliography contains recent references.Besides industrial and Berlin-airlift scheduling problems, the book contains TSP examples of circuit-board wiring, U.S. state capitals, and Odysseus!

Three more highlights: The double description algorithm receives a complete description, and this is useful for combinatorial geometers.The discussion of integer-arithmetic and complexity theory is very readable, and these technical topics are slighted by interior-point books (besides Wright's quickie), despite their importance in integer programming and combinatorial optimization. The discussion of interior-point algorithms emphasizes projective geometry, a beautiful theory that has inspired so much of optimization theory---besides Karmarkar's interior-point algorithm,Dantzig's simplex algorithm, Fenchel duality, Davidon's conic algorithm for nonlinear optimization, etc.).

The book is not a comprehensive survey of linear programming,
and lacks a treatment of Nesterov's theory of self-concordant barrier-functions.Also, no treatment is given of pivoting algorithms besides Dantzig's (e.g., Terlaky's criss-cross method, Todd's oriented matroid algorithm).

A good reference for Linear Programming Theory
This book is certainly a very good reference for theoretical topics of linear programming. It covers the Simplex method and the Ellipsoid algorithms. It also covers the geometry of linear programming (polyhedraand polytopes, etc). It certainly covers more topics than most other linearprogramming texts.As expected, a book writen for theoretical topics iscertainly not easy to read, especially for people with no training in doingrigorous mathematical proofs. Also, not many examples or illustrations aregiven in this book, and this might be a problem for some readers. ... Read more

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This monograph develops projective geometries and provides asystematic treatment of morphisms. It is unique in that it does notconfine itself to isomorphisms. This work introduces a new fundamentaltheorem and its applications describing homogeneous coordinates asmorphisms of projective geometries by semilinear maps. Other topicstreated include three equivalent definitions of projective geometriesand their correspondence with certain lattices; quotients ofprojective geometries and isomorphism theorems; recent results indimension theory; morphisms and homomorphisms of projectivegeometries; special morphisms; duality theory; morphisms of affinegeometries; polarities; orthogonalities; Hilbertian geometries andpropositional systems. The book concludes with a large section ofexercises.

Audience: This volume will be of interest to mathematicians andresearchers whose work involves projective geometries and theirmorphisms, semilinear maps and sesquilinear forms, lattices, categorytheory, and quantum mechanics. This book can also be recommended as atext in axiomatic geometry. ... Read more

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Applied Mathematics: Body & Soul is a mathematics education reform project developed at Chalmers University of Technology and includes a series of volumes and software. The program is motivated by the computer revolution opening new possibilities of computational mathematical modeling in mathematics, science and engineering. It consists of a synthesis of Mathematical Analysis (Soul), Numerical Computation (Body) and Application. Volumes I-III present a modern version of Calculus and Linear Algebra, including constructive/numerical techniques and applications intended for undergraduate programs in engineering and science. Further volumes present topics such as Dynamical Systems, Fluid Dynamics, Solid Mechanics and Electro-Magnetics on an advanced undergraduate/graduate level.

The authors are leading researchers in  Computational Mathematics who have written various successful books.

Product Description

Applied Mathematics: Body & Soul is a mathematics education reform project developed at Chalmers University of Technology and includes a series of volumes and software. The program is motivated by the computer revolution opening new possibilitites of computational mathematical modeling in mathematics, science and engineering. It consists of a synthesis of Mathematical Analysis (Soul), Numerical Computation (Body) and Application. Volumes I-III present a modern version of Calculus and Linear Algebra, including constructive/numerical techniques and applications intended for undergraduate programs in engineering and science. Further volumes present topics such as Dynamical Systems, Fluid Dynamics, Solid Mechanics and Electro-Magnetics on an advanced undergraduate/graduate level.

The authors are leading researchers in Computational Mathematics who have written various successful books.

Product Description

This is a self-contained introduction to algebraic control for nonlinear systems suitable for researchers and graduate students. It is the first book dealing with the linear-algebraic approach to nonlinear control systems in such a detailed and extensive fashion. It provides a complementary approach to the more traditional differential geometry and deals more easily with several important characteristics of nonlinear systems.

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This book is the first comprehensive treatment of rational matrix equations in stochastic systems, including various aspects of the field, previously unpublished results and explicit examples. Topics include modelling with stochastic differential equations, stochastic stability, reformulation of stochastic control problems, analysis of the rational matrix equation and numerical solutions. Primarily a survey in character, this monograph is intendedfor researchers, graduate students and engineers in control theory and applied linear algebra. ... Read more

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Matrix and polynomial computations are fundamental to the theory and practice of computing. The authors present here a systematic treatment of algorithms and complexity in these two related areas. Its study of computations with Toeplitz matrices and other dense structured matrices demonstrates the links between numerical and algebraic approaches to computation. The authors begin with classical fundamental problems and gradually introduce the reader to current research. In particular, the book provides improved parallel algorithms for computations with structured matrices and their further applications to some fundamental computations with matrices and polynomials. The book is designed as a text for advanced graduates in mathematics and computer science. ... Read more

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This volume deals both with the finite-dimensional and the compact theorems about triangularization. It is designed to appeal to two different audiences. The first four chapters should be of interest to linear-algebraists and other algebraists (e.g. people interested in finite-dimensional representations) who use algebras or semigroups of matrices. These chapters include new appraoches to some results that are widely used, as well as recent developments and extensions. The remaining chapters concerned with the structures of linear operators on Banach spaces will attract operator theorists. The most satisfactory results are obtained for algebras and semigroups of compact operators. These theorems, based on the funamental work of Lomonsov and Ringrose of twenty-five years ago, are all quite recent. A number of important questions remain open; the authors hope that their presentation will stimulate further research. ... Read more

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Das Computeralgebrasystem MuPAD ist eines der unentbehrlichen Werkzeuge für Lehre und Forschung in den Natur- und Ingenieurwissenschaften. Es überzeugt durch klare Strukturen, vielfältige Visualisierungsmöglichkeiten und effiziente Berechnungen. Diese kompakte, übersichtliche und elementare Einführung demonstriert anhand vieler Beispiele den Aufbau der Sprache und ihre wichtigsten Sprachelemente – basierend auf der MuPAD-Version Pro 4.0.

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This book addresses a new method for generating tight linear orconvex programming relaxations for discrete and continuous nonconvexprogramming problems. Problems of this type arise in many economics,location-allocation, scheduling and routing, and process control andengineering design applications. The principal thrust is to commencewith a model that affords a useful representation and structure, andthen to further strengthen this representation through an automaticreformulation and constraint generation technique. The contents ofthis book comprise the original work of the authors compiled fromseveral journal publications, and not covered in any other book onthis subject. The outstanding feature of this book is that it offersfor the first time a unified treatment of discrete and continuousnonconvex programming problems. In essence, the bridge between thesetwo types of nonconvexities is made via a polynomial representation ofdiscrete constraints. The book lays the foundation of an idea that isstimulating and that has served to enhance the solubility of manychallenging problems in the field.
Audience: This book is intended for researchers andpractitioners who work in the area of discrete or continuousnonlinear, nonconvex optimization problems, as well as for studentswho are interested in learning about techniques for solving suchproblems. ... Read more

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The first chapter of this book provides a brief treatment ofthe basics of the subject. The other chapters deal with the variousdecompositions of non-negative matrices, Birkhoff type theorems, thestudy of the powers of non-negative matrices, applications of matrixmethods to other combinatorial problems, and applications ofcombinatorial methods to matrix problems and linear algebra problems.

The coverage of prerequisites has been kept to a minimum.Nevertheless, the book is basically self-contained (an Appendixprovides the necessary background in linear algebra, graph theory andcombinatorics). There are many exercises, all of which are accompaniedby sketched solutions. Audience: The book is suitable for a graduate course as well asbeing an excellent reference and a valuable resource formathematicians working in the area of combinatorial matrix theory. ... Read more

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Written by one of the top experts in the fields of combinatorics and representation theory, this book distinguishes itself from the existing literature by its applications-oriented point of view. The second edition is extended, placing more emphasis on applications to the constructive theory of finite structures. Recent progress in this field, in particular in design and coding theory, is described.

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This volume contains articles that document the advances in thesubject of Total Positivity during the last two decades. The materialis divided into ten chapters. While some of the articles are of asurvey nature, others present new results appearing here for the firsttime. Also, some papers contain introductory material and aretherefore accessible to non-experts interested in becoming familiarwith the important ideas and techniques of Total Positivity.
Audience: This book will be of value to mathematicians,engineers and computer scientists whose work involves applications ofTotal Positivity to problems in the theory of spline functions,numerical quadrature, nonlinear analysis, entire functions,probability, mathematical biology, statistics, approximation theory,combinatorics, geometric modelling, matrix theory and integralequations. ... Read more

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This volume contains a facsimile reproduction of Marcel Riesz'snotes of a set of lectures he delivered at the University of Maryland,College Park, between October 1957 and January 1958, which has notbeen formally published to date. This seminal material (arranged infour chapters), which contributed greatly to the start of modernresearch on Clifford algebras, is supplemented in this book by noteswhich Riesz dictated to E. Folke Bolinder in the following year andwhich were intended to be a fifth chapter of the Riesz lecture notes.In addition, Riesz's work on Clifford algebra is put into anhistorical perspective in a separate review by P. Lounesto.
As well as providing an introduction to Clifford algebra, this volumewill be of value to those interested in the history ofmathematics.
... Read more

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Statistical Analysis of Observations of IncreasingDimension is devoted to the investigation of the limitdistribution of the empirical generalized variance, covariancematrices, their eigenvalues and solutions of the system of linearalgebraic equations with random coefficients, which are an importantfunction of observations in multidimensional statistical analysis. Ageneral statistical analysis is developed in which observed randomvectors may not have density and their components have an arbitrarydependence structure. The methods of this theory have very importantadvantages in comparison with existing methods of statisticalprocessing. The results have applications in nuclear and statisticalphysics, multivariate statistical analysis in the theory of thestability of solutions of stochastic differential equations, incontrol theory of linear stochastic systems, in linear stochasticprogramming, in the theory of experiment planning.
... Read more

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The main purpose of this monograph is to report on recent developments in the field of matrix inequalities, with emphasis on useful techniques and ingenious ideas. Among other results this book contains the affirmative solutions of eight conjectures. Many theorems unify or sharpen previous inequalities. The author's aim is to streamline the ideas in the literature. The book can be read by research workers, graduate students and advanced undergraduates. ... Read more

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Time-Varying Systems and Computations is a unique bookproviding a detailed and consistent exposition of a powerful unifyingframework (developed by the authors) for the study of time-variantsystems and the computational aspects and problems that arise in thiscontext. While complex function theory and linear algebra provide muchof the fundamental mathematics needed by engineers engaged innumerical computations, signal processing and/or control, there haslong been a large, abstruse gap between the two fields. This bookshows the reader how the gap between analysis and linear algebra canbe bridged. In a fascinating monograph, the authors explore, discoverand exploit many interesting links that exist between classical linearalgebraic concepts and complex analysis.
Time-Varying Systems and Computations opens for the reader newand exciting perspectives on linear algebra from the analysis point ofview. It clearly explains a framework that allows the extension ofclassical results, from complex function theory to the case oftime-variant operators and even finite-dimensional matrices. Theseresults allow the user to obtain computationally feasible schemes andmodels for complex and large-scale systems.
Time-Varying Systems and Computations will be of interest to abroad spectrum of researchers and professionals, including appliedmathematicians, control theorists, systems theorists and numericalanalysts. It can also be used as a graduate course in lineartime-varying system theory. ... Read more

Customer Reviews (1)

Treasure Trove for advanced theory on lin ear systems
This is definitely an outstanding book on linear time-varying systems. It contains a substantial amount of original work and results compiled in a compact way nowhere else to be found. The book is heavy on the theoretical side and not very close to applications. If You are searching for a book containing recipes for your every day problems - forget it. If search for a book that provides You with in depth descriptions on a mathematically challenging topic - You found it. A last note - in spite of the great contents it is a tough read, even for experts in the field. So beware and enjoy. ... Read more

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This volume contains selected papers by Torben Krarup, one of the most important geodesists of the 20th century. The collection includes the famous booklet "A Contribution to the Mathematical Foundation of Physical Geodesy" from 1969, the unpublished "Molodenskij letters" from 1973, the final version of "Integrated Geodesy" from 1978, "Foundation of a Theory of Elasticity for Geodetic Networks" from 1974, as well as trend-setting papers on the theory of adjustment.

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Discrete-time systems arise as a matter of course in modelling biological or economic processes. For systems and control theory they are of major importance, particularly in connection with digital control applications. If sampling is performed in order to control periodic processes, almost periodic systems are obtained. This is a strong motivation to investigate the discrete-time systems with time-varying coefficients. This research monograph contains a study of discrete-time nodes, the discrete counterpart of the theory elaborated by Bart, Gohberg and Kaashoek for the continuous case, discrete-time Lyapunov and Riccati equations, discrete-time Hamiltonian systems in connection with input-output operators and associated Hankel and Toeplitz operators. All these tools aim to solve the problems of stabilization and attenuation of disturbances in the framework of H2- andH-control theory. The book is the first of its kind to be devoted to these topics and consists mainly of original, recently obtained results. ... Read more