Download or read book Time Variant Systems and Interpolation written by I. Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Time Varying Systems and Computations written by Patrick DeWilde and published by Springer Science & Business Media. This book was released on 1998-06-30 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex function theory and linear algebra provide much of the basic mathematics needed by engineers engaged in numerical computations, signal processing or control. The transfer function of a linear time invariant system is a function of the complex vari able s or z and it is analytic in a large part of the complex plane. Many important prop erties of the system for which it is a transfer function are related to its analytic prop erties. On the other hand, engineers often encounter small and large matrices which describe (linear) maps between physically important quantities. In both cases similar mathematical and computational problems occur: operators, be they transfer functions or matrices, have to be simplified, approximated, decomposed and realized. Each field has developed theory and techniques to solve the main common problems encountered. Yet, there is a large, mysterious gap between complex function theory and numerical linear algebra. For example, complex function theory has solved the problem to find analytic functions of minimal complexity and minimal supremum norm that approxi e. g. , as optimal mate given values at strategic points in the complex plane. They serve approximants for a desired behavior of a system to be designed. No similar approxi mation theory for matrices existed until recently, except for the case where the matrix is (very) close to singular.

Download or read book Time Varying Discrete Linear Systems written by Aristide Halanay and published by Birkhäuser. This book was released on 2012-12-06 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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- and H-control theory. The book is the first of its kind to be devoted to these topics and consists mainly of original, recently obtained results.

Download or read book Operator Theory System Theory and Related Topics written by Daniel Alpay and published by Springer Science & Business Media. This book was released on 2001-03-01 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the refereed proceedings of the Conference in Operator The ory in Honour of Moshe Livsic 80th Birthday, held June 29 to July 4, 1997, at the Ben-Gurion University of the Negev (Beer-Sheva, Israel) and at the Weizmann In stitute of Science (Rehovot, Israel). The volume contains papers in operator theory and its applications (understood in a very wide sense), many of them reflecting, 1 directly or indirectly, a profound impact of the work of Moshe Livsic. Moshe (Mikhail Samuilovich) Livsic was born on July 4, 1917, in the small town of Pokotilova near Uman, in the province of Kiev in the Ukraine; his family moved to Odessa when he was four years old. In 1933 he enrolled in the Department of Physics and Mathematics at the Odessa State University, where he became a student of M. G. Krein and an active participant in Krein's seminar - one of the centres where the ideas and methods of functional analysis and operator theory were being developed. Besides M. G. Krein, M. S. Livsic was strongly influenced B. Va. Levin, an outstanding specialist in the theory of analytic functions. A by deep understanding of operator theory as well as function theory and a penetrating search of connections between the two, were to become one of the landmarks of M. S. Livsic's work. M. S. Livsic defended his Ph. D.

Download or read book Operator Theory and Analysis written by H. Bart and published by Birkhäuser. This book was released on 2012-12-06 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: On November 12-14, 1997 a workshop was held at the Vrije Universiteit Amsterdam on the occasion of the sixtieth birthday ofM. A. Kaashoek. The present volume contains the proceedings of this workshop. The workshop was attended by 44 participants from all over the world: partici pants came from Austria, Belgium, Canada, Germany, Ireland, Israel, Italy, The Netherlands, South Africa, Switzerland, Ukraine and the USA. The atmosphere at the workshop was very warm and friendly. There where 21 plenary lectures, and each lecture was followed by a lively discussion. The workshop was supported by: the Vakgroep Wiskunde of the Vrije Univer siteit, the department of Mathematics and Computer Science of the Vrije Univer siteit, the Stichting VU Computer Science & Mathematics Research Centre, the Thomas Stieltjes Institute for Mathematics, and the department of Economics of the Erasmus University Rotterdam. The organizers would like to take this opportunity to express their gratitude for the support. Without it the workshop would not have been so successful as it was. Table of Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Photograph of M. A. Kaashoek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Curriculum Vitae of M. A. Kaashoek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv List of Publications of M. A. Kaashoek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix l. Gohberg Opening Address . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxi H. Bart, A. C. M. Ran and H. I. Woerdeman Personal Reminiscences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxv V. Adamyan and R. Mennicken On the Separation of Certain Spectral Components of Selfadjoint Operator Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Conditions for the Separation of Spectral Components . . . . . . . 4 3. Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Download or read book Contributions to Operator Theory in Spaces With an Indefinite Metric written by H. Langer and published by Springer Science & Business Media. This book was released on 1998 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Heinz Langer, a leading expert in spectral analysis and its applications, in particular to operators in spaces with an indefinite metric, on the occasion of his 60th birthday. The book begins with his biography and list of publications. It contains a selection of research papers, most of which are devoted to spectral analysis of operators or operator pencils with applications to ordinary and partial differential equations. Other papers deal with time-varying systems, interpolation and factorization problems, and topics from mathematical physics. About half of the papers contain further developments in the theory of operators in spaces with an indefinite metric and treat new applications. The book is of interest to a wide audience of pure and applied mathematicians.

Download or read book Constrained Control of Uncertain Time Varying Discrete Time Systems written by Hoai-Nam Nguyen and published by Springer. This book was released on 2013-12-11 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive development of interpolating control, this monograph demonstrates the reduced computational complexity of a ground-breaking technique compared with the established model predictive control. The text deals with the regulation problem for linear, time-invariant, discrete-time uncertain dynamical systems having polyhedral state and control constraints, with and without disturbances, and under state or output feedback. For output feedback a non-minimal state-space representation is used with old inputs and outputs as state variables. Constrained Control of Uncertain, Time-Varying, Discrete-time Systems details interpolating control in both its implicit and explicit forms. In the former at most two linear-programming or one quadratic-programming problem are solved on-line at each sampling instant to yield the value of the control variable. In the latter the control law is shown to be piecewise affine in the state, and so the state space is partitioned into polyhedral cells so that at each sampling interval the cell to which the measured state belongs must be determined. Interpolation is performed between vertex control, and a user-chosen control law in its maximal admissible set surrounding the origin. Novel proofs of recursive feasibility and asymptotic stability of the vertex control law, and of the interpolating control law are given. Algorithms for implicit and explicit interpolating control are presented in such a way that the reader may easily realize them. Each chapter includes illustrative examples, and comparisons with model predictive control in which the disparity in computational complexity is shown to be particularly in favour of interpolating control for high-order systems, and systems with uncertainty. Furthermore, the performance of the two methods proves similar except in those cases when a solution cannot be found with model predictive control at all. The book concludes with two high dimensional examples and a benchmark robust model predictive control problem: the non-isothermal continuously-stirred-tank reactor. For academic control researchers and students or for control engineers interested in implementing constrained control systems Constrained Control of Uncertain, Time-Varying, Discrete-time Systems will provide an attractive low-complexity control alternative for cases in which model predictive control is currently attempted.

Download or read book Time Varying Systems and Computations written by Patrick DeWilde and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex function theory and linear algebra provide much of the basic mathematics needed by engineers engaged in numerical computations, signal processing or control. The transfer function of a linear time invariant system is a function of the complex vari able s or z and it is analytic in a large part of the complex plane. Many important prop erties of the system for which it is a transfer function are related to its analytic prop erties. On the other hand, engineers often encounter small and large matrices which describe (linear) maps between physically important quantities. In both cases similar mathematical and computational problems occur: operators, be they transfer functions or matrices, have to be simplified, approximated, decomposed and realized. Each field has developed theory and techniques to solve the main common problems encountered. Yet, there is a large, mysterious gap between complex function theory and numerical linear algebra. For example, complex function theory has solved the problem to find analytic functions of minimal complexity and minimal supremum norm that approxi e. g. , as optimal mate given values at strategic points in the complex plane. They serve approximants for a desired behavior of a system to be designed. No similar approxi mation theory for matrices existed until recently, except for the case where the matrix is (very) close to singular.

Download or read book Modeling and Identification of Linear Parameter Varying Systems written by Roland Toth and published by Springer. This book was released on 2010-07-11 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through the past 20 years, the framework of Linear Parameter-Varying (LPV) systems has become a promising system theoretical approach to handle the control of mildly nonlinear and especially position dependent systems which are common in mechatronic applications and in the process industry. The birth of this system class was initiated by the need of engineers to achieve better performance for nonlinear and time-varying dynamics, c- mon in many industrial applications, than what the classical framework of Linear Time-Invariant (LTI) control can provide. However, it was also a p- mary goal to preserve simplicity and “re-use” the powerful LTI results by extending them to the LPV case. The progress continued according to this philosophy and LPV control has become a well established ?eld with many promising applications. Unfortunately, modeling of LPV systems, especially based on measured data (which is called system identi?cation) has seen a limited development sincethebirthoftheframework. Currentlythisbottleneck oftheLPVfra- work is halting the transfer of the LPV theory into industrial use. Without good models that ful?ll the expectations of the users and without the und- standing how these models correspond to the dynamics of the application, it is di?cult to design high performance LPV control solutions. This book aims to bridge the gap between modeling and control by investigating the fundamental questions of LPV modeling and identi?cation. It explores the missing details of the LPV system theory that have hindered the formu- tion of a well established identi?cation framework.

Download or read book Structured Matrices in Mathematics Computer Science and Engineering I written by Vadim Olshevsky and published by American Mathematical Soc.. This book was released on 2001 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The collection of the contributions to these volumes offers a flavor of the plethora of different approaches to attack structured matrix problems. The reader will find that the theory of structured matrices is positioned to bridge diverse applications in the sciences and engineering, deep mathematical theories, as well as computational and numberical issues. The presentation fully illustrates the fact that the technicques of engineers, mathematicisn, and numerical analysts nicely complement each other, and they all contribute to one unified theory of structured matrices"--Back cover.

Download or read book Operator Algebras Operator Theory and Applications written by J. J. Grobler and published by Springer Science & Business Media. This book was released on 2009-12-24 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the eighteenth International Workshop on Operator Theory and Applications (IWOTA), hosted by the Unit for Business Mathematics and Informatics of North-West University, Potchefstroom, South Africa from July 3 to 6, 2007. The conference (as well as these proceedings) was dedicated to Professors Joseph A. Ball and Marinus M. Kaashoek on the occasion of their 60th and 70th birthdays, respectively. This conference had a particular focus on Von Neumann algebras at the interface of operator theory with functional analysis and on applications of operator theory to differential equations.

Download or read book Time varying System Theory and Computational Modeling written by Alle-Jan van der Veen and published by . This book was released on 1993 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Issues in Logic Operations and Computational Mathematics and Geometry 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 995 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Logic, Operations, and Computational Mathematics and Geometry. The editors have built Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Logic, Operations, and Computational Mathematics and Geometry in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Download or read book The Schur Algorithm Reproducing Kernel Spaces and System Theory written by Daniel Alpay and published by American Mathematical Soc.. This book was released on 2001 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: The class of Schur functions consists of analytic functions on the unit disk that are bounded by $1$. The Schur algorithm associates to any such function a sequence of complex constants, which is much more useful than the Taylor coefficients. There is a generalization to matrix-valued functions and a corresponding algorithm. These generalized Schur functions have important applications to the theory of linear operators, to signal processing and control theory, and to other areas of engineering. In this book, Alpay looks at matrix-valued Schur functions and their applications from the unifying point of view of spaces with reproducing kernels. This approach is used here to study the relationship between the modeling of time-invariant dissipative linear systems and the theory of linear operators. The inverse scattering problem plays a key role in the exposition. The point of view also allows for a natural way to tackle more general cases, such as nonstationary systems, non-positive metrics, and pairs of commuting nonself-adjoint operators. This is the English translation of a volume originally published in French by the Societe Mathematique de France. Translated by Stephen S. Wilson.

Download or read book Recent Advances in Operator Theory written by A. Dijksma and published by Birkhäuser. This book was released on 2012-12-06 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of 25 papers dedicated to Israel Gohberg, an outstanding leader in operator theory. Also containing a review of his contributions to mathematics and a complete list of his publications. The book is of interest to a wide audience of pure and applied mathematicians.

Download or read book Slice Hyperholomorphic Schur Analysis written by Daniel Alpay and published by Birkhäuser. This book was released on 2016-12-09 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book defines and examines the counterpart of Schur functions and Schur analysis in the slice hyperholomorphic setting. It is organized into three parts: the first introduces readers to classical Schur analysis, while the second offers background material on quaternions, slice hyperholomorphic functions, and quaternionic functional analysis. The third part represents the core of the book and explores quaternionic Schur analysis and its various applications. The book includes previously unpublished results and provides the basis for new directions of research.

Download or read book Metric Constrained Interpolation Commutant Lifting and Systems written by Ciprian Foiaş and published by Springer Science & Business Media. This book was released on 1998 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Interpolation And Time-Invariant Systems.- I. Interpolation Problems For Operator-Valued Functions.- 1.1. Preliminaries About Notation And Terminology.- 1.2. Nevanlinna-Pick Interpolation.- 1.3. Tangential Nevanlinna-Pick Interpolation.- 1.4. Controllability Operators And Interpolation.- 1.5. Tangential Hermite-Fejer Interpolation.- 1.6. The Nehari Extension Problem.- 1.7. Sarason Interpolation.- 1.8. Nevanlinna-Pick Interpolation Viewed As A Sarason Problem.- 1.9. Two-Sided Nudelman Interpolation.- 1.10. The Two-Sided Sarason Problem.- 1.11. A Filtering Problem.- Notes To Chapter I.- II. Proofs Using The Commutant Lifting Theorem.- II.1. The Commutant Lifting Theorem.- II.2. Proof Of The Standard Left Nevanlinna-Pick Interpolation Theorem.- II.3. Proof Of The Nehari Extension Theorem.- II.4. Proof of the Sarason Theorem.- II.5. Proof of the Two-Sided Nudelman Theorem.- II.6. Proof of the Two-Sided Sarason Theorem.- Notes to Chapter II.- III. Time Invariant Systems.- III.1. State Space Analysis.- III.2. Controllability and Observability.- III.3. Point Evaluation.- III.4. Realization Theory.- III.5. Anticausal Realizations.- III.6. Computing the Hankel form.- III.7. Computing the Projection in the Sarason Problem.- III.8. Explicit Conversion Formulas.- III.9. Connecting Nudelman and Two-Sided Sarason Problems.- III.10. Isometric and Unitary Systems.- Notes to Chapter III.- IV. Central Commutant Lifting.- IV. 1. Minimal Isometric Liftings.- IV.2. The Central Intertwining Lifting.- IV.3. Central Intertwining Lifting Formulas.- IV.4. Central Intertwining Lifting Quotient Formulas.- IV.5. The Central Schur Solution.- IV.6. The Quasi Outer Factor for D2/By.- IV.7. Maximum Entropy.- IV.8. Some Mixed Bounds for the Central Intertwining Lifting.- IV.9. A Mixed Two-Sided Sarason Result.- Notes To Chapter IV.- V. Central State Space Solutions.- V.1. The Central Formula For Nevanlinna-Pick.- V.2. Central Nevanlinna-Pick Solutions.- V.3. The Central Hermite-Fejer Solution.- V.4. The Central Formula For The Sarason Problem.- V.5. Central Nehari Solutions.- V.6. Central Nudelman Solutions.- V.7. The Central Two Block Solution.- V.8. The Four Block Problem.- Notes To Chapter V.- VI. Parameterization Of Intertwining Liftings And Its Applications.- VI.1. The Möbius Transformation.- VI.2. The Schur Parameterization.- VI.3. Recovering The Schur Contraction..- VI. 4. Constructing The Schur Contraction.- VI.5. The Redheffer Scattering Parameterization.- VI.6. The Parameterization for A ?.- VI.7. The Nevalinna-Pick Parameterization.- VI.8. The Nehari Parameterization.- VI.9. The Two Block Parameterization.- Notes To Chapter VI.- VII. Applications to Control Systems.- VII. 1. Feedback Control.- VII.2. The Youla Parameterization.- VII.3. Mixed H? and H2 Control Problems.- VII.4. A Two Block Control Problem.- VII.5. The Multivariable Case.- Notes To Chapter VII.- B Nonstationary Interpolation and Time-Varying Systems.- VIII. Nonstationary Interpolation Theorems.- VIII.1. Nonstationary Nevanlinna-Pick Interpolation.- VIII.2. Nonstationary Tangential Nevanlinna-Pick Interpolation.- VIII.3. Nonstationary Tangential Hermite-Fejer Interpolation.- VIII.4. Nonstationary Nehari Interpolation.- VIII.5. Nonstationary Sarason Interpolation.- VIII.6. Nonstationary Nudelman Interpolation.- VIII.7. Nonstationary Two-Sided Sarason Interpolation.- Notes to Chapter VIII.- IX. Nonstationary Systems and Point Evaluation.- IX.1. Time Varying Systems.- IX.2. Nonstationary Controllability and Observability.- IX.3. Point Evaluation.- IX.4. From Nonstationary Systems to Stationary Systems.- IX.5. A Nonstationary Filtering Problem.- Notes to Chapter IX.- X. Reduction Techniques: From Nonstationary to Stationary and Vice Versa.- X.1. Spatial Features.- X.2. Operator Features.- Notes to Chapter X.- XI. Proofs of the Nonstationary Interpolation Theorems by Reduction to the Stationary Case.- XI.1. The Standard Nonstationary Nevanlinna-Pick Interpolation Theorem.- XI.2. The Nons