Heij, Christiaan, Ran, Andre C.M., Schagen, F. van

Introduction to Mathematical Systems Theory
Linear Systems, Identification and Control

2006, 200 p., Softcover
ISBN: 3-7643-7548-5

About this textbook

The purpose of this book is to provide an introduction to the theory of linear systems and control for students in business mathematics, econometrics, computer science, and engineering. The subjects treated are for one the central topics from deterministic linear system theory, i.e. controllability, observability, realization theory, stability and stabilization by feedback, LQ-optimal control theory. Kalman filtering and LQC-control of stochastic systems are also discussed. Finally, attention is paid to modelling, e.g. time series analysis and model specification, along with model validation. All topics in the book are supported by exercises requiring the use of Matlab, which illustrate and enhance the main concepts and techniques in the text.

Written for:

Students with interest in quantitative methods and dynamic decision making in the fields of business mathematics, economics, and econometrics

students in mathematics, engineering, and life sciences.

Keywords:
Control theory
Filtering
Linear systems
Model validation
Stability
Stochastic systems
Systems theory
Time series analysis

Grigoryan, Suren A., Tonev, Thomas V.

Shift-invariant Uniform Algebras on Groups

Series: Monografie Matematyczne, Vol. 68
2006, Approx. 300 p., Hardcover
ISBN: 3-7643-7606-6

About this book

The central subject of the book - the theory of shift-invariant algebras - is an outgrowth of the established theory of generalized analytic functions. Associated subalgebras of almost periodic functions of real variables and of bounded analytic functions on the unit disc are carried along within the general framework. In particular, it is shown that the algebra of almost periodic functions with spectrum in a semigroup of the reals does not have a half-plane-corona if and only if all non-negative semicharacters of the semigroup are monotone decreasing, or equivalently, if and only if the strong hull of the semigroup coincides with the positive half of its group envelope. Under the same conditions the corresponding subalgebra of bounded analytic functions on the disc has neither a half-plane-corona nor a disc-corona. There are given characterizations of semigroups such that classical theorems of complex analysis hold on the associated shift-invariant algebras. Bourgain algebras, orthogonal measures, and primary ideals of big disc algebras are described. The notion of a harmonic function is extended on compact abelian groups, and corresponding Fatou-type theorems are proven. Important classes of inductive limits of standard uniform algebras, including Blasche algebras, are introduced and studied. In particular, it is shown that algebras of hyper-analytic functions, associated with families of inner functions, do not have a big-disc-corona.

Written for:

Mathematicians interested in analytic functions and commutative Banach algebras; researchers, graduate and post-graduate students familiar only with the fundamentals of complex and functional analysis

Table of contents

Preface.- 1. Banach Algebras and Uniform Algebras.- 2. Three Classical Families of Functions.- 3. Groups and Semigroups.- 4. Shift-invariant Algebras on Compact Groups.- 5. Extension of Semicharacters and Additive Weights.- 6. G-disc Algebras.- 7. Harmonicity on Groups and G-discs.- 8. Shift-invariant Algebras and Inductive Limit Algebras on Groups.- Bibliography.- Index.

Triebel, Hans

Theory of Function Spaces III

Series: Monographs in Mathematics, Vol. 100
2006, Approx. 445 p., Hardcover
ISBN: 3-7643-7581-7
A Birkhauser book

About this book

This volume presents the recent theory of function spaces paying special attention to some developments in the last 10-15 years related to neighbouring areas such as numerics, signal processing, fractal analysis, etc. Local building blocks, in particular (non-smooth) atoms, quarks, wavelet bases and wavelet frames will be considered in detail and applied afterwards to diverse problems, including a local smoothness theory, spaces on Lipschitz domains, and fractal analysis.

The book is essentially self-contained, although it might be also considered as the continuation of the two books of the author with the same title.

Written for:

Mathematicians interested in analysis, numerics, or fractal geometry

Table of contents

Preface.- 1. How to Measure Smoothness.- 2. Atoms and Pointwise Multipliers.- 3. Wavelets.- 4. Spaces on Domains, Wavelets, Sampling Numbers.- 5. Anisotropic Function Spaces.- 6. Weighted Function Spaces.- 7. Fractal Analysis.- 8. Function Spaces on Quasi-metric Spaces.- 9. Function Spaces on Sets.- References.- Notation, Symbols.- Index.

Amann, Herbert, Escher, Joachim

Analysis II

2006, Approx. 420 p., Softcover
ISBN: 3-7643-7472-1

About this textbook

The second volume of this introduction into analysis deals with the integration theory of functions of one variable, the multidimensional differential calculus and the theory of curves and line integrals. The modern and clear development that started in Volume I (3-7643-7153-6) continues. In this way a sustainable basis will be created which allows to deal with interesting applications that sometimes go considerably beyond the material that is represented in traditional textbooks. This applies, for instance, to the exploration of Nemytskii operators which enable a transparent introduction into the calculus of variations and the derivation of the Euler-Lagrange equations. Another example is the presentation of the local theory of submanifolds of Rn.

Written for:

Advanced undergraduate and graduate students; advisors; teachers

Table of contents

Preface.- VI. Integral Calculus in One Variable - 1. Step Continuous Functions - 2. Continuous Extensions - 3. The Cauchy-Riemann Integral - 4. Properties of the Integral - 5. The Technology of Integration - 6. Sums and Integrals - 7. Fourier Series - 8. Improper Integrals - 9. The Gamma Function.- VII. Differential Calculus in Several Variables - 1. Continuous Linear Mappings - 2. Differentiability - 3. Calculation Rules - 4. Multilinear Mappings - 5. Higher Derivatives - 6. Nemytski Operators and Calculus of Variations - 7. Inverse Mappings - 8. Implicit Functions - 9. Manifolds - 10. Tangents and Normals.- VIII. Line Integrals - 1. Curves and Their Length - 2. Curves in Rn - 3. Pfaff Forms - 4. Line Integrals - 5. Holomorphic Functions - 6. Meromorphic Functions.- Bibliography.- Index.

Antsaklis, Panos J., Michel, Anthony N.

A Linear Systems Primer

2007, Approx. 415 p. 50 illus., Softcover
ISBN: 0-8176-4460-1

About this textbook

Based on a streamlined presentation of the authors’ successful work Linear Systems, this textbook provides an introduction to systems theory with an emphasis on control. The material presented is broad enough to give the reader a clear picture of the dynamical behavior of linear systems as well as their advantages and limitations. Fundamental results and topics essential to linear systems theory are emphasized.

Table of contents

Background Material: Differential Equations and Initial Value Problems.- Descriptions of Dynamical Systems.- Background Material: Algebra.- Response of Time-Invariant Linear Systems.- Stability.- Controllability and Observability: Fundamental Results.- Controllability and Observability: Special Forms.- Relations Between Internal and External Descriptions.- Realizations: Theory and Algorithms.- State Feedback and State Observers.- Control Design: Geometric Approach.- Control Design: Coprime Factorizations.- Appendix A: Numerical Considerations.- Appendix B: Polynomial Matrices.- Index