Author: Patrick DeWilde Publisher: Springer Science & Business Media ISBN: 9780792381891 Category : Science Languages : en Pages : 494
Book Description
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.
Author: Patrick DeWilde Publisher: Springer Science & Business Media ISBN: 1475728174 Category : Science Languages : en Pages : 457
Book Description
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.
Author: Aristide Halanay Publisher: Birkhäuser ISBN: 3034884990 Category : Mathematics Languages : en Pages : 237
Book Description
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.
Author: Daniel Alpay Publisher: Springer Science & Business Media ISBN: 9783764365233 Category : Mathematics Languages : en Pages : 596
Book Description
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.
Author: Harry Dym Publisher: Springer Science & Business Media ISBN: 3034804113 Category : Mathematics Languages : en Pages : 364
Book Description
This volume is dedicated to Bill Helton on the occasion of his sixty fifth birthday. It contains biographical material, a list of Bill's publications, a detailed survey of Bill's contributions to operator theory, optimization and control and 19 technical articles. Most of the technical articles are expository and should serve as useful introductions to many of the areas which Bill's highly original contributions have helped to shape over the last forty odd years. These include interpolation, Szegö limit theorems, Nehari problems, trace formulas, systems and control theory, convexity, matrix completion problems, linear matrix inequalities and optimization. The book should be useful to graduate students in mathematics and engineering, as well as to faculty and individuals seeking entry level introductions and references to the indicated topics. It can also serve as a supplementary text to numerous courses in pure and applied mathematics and engineering, as well as a source book for seminars.
Author: Ciprian Foiaş Publisher: Springer Science & Business Media ISBN: 9783764358891 Category : Computers Languages : en Pages : 610
Book Description
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
Author: Roland Toth Publisher: Springer ISBN: 3642138128 Category : Technology & Engineering Languages : en Pages : 337
Book Description
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.