Synopses & Reviews
This new edited book focuses on the contemporary developments and results in mathematical systems theory and control. It is a book in honor of Diederich Hinrichsen, for his fundamental contributions and achievements in the fields of linear systems theory and control theory and for his long term achievements in establishing mathematical systems theory in Germany. The book includes invited, peer-reviewed, authoritative expositions and surveys of these fields, presented by leading international researchers. A key theme of the book is the stability and robustness of linear and nonlinear systems using the concepts of stability radii and spectral value sets. Chapters survey recent advances in linear and nonlinear systems theory, including parameterization problems and behaviors of linear systems, convolutional codes, and complementary systems and hybrid systems. In addition, the volume examines controllability and stabilization of infinite dimensional systems (allowing for hysteresis nonlinearities) with functional analytic and algebraic approaches. Features and topics include: * linear and nonlinear systems theory * control theory and applications * robust stability of multivariate polynomials * stability radii of slowly time-varying systems * invariance radius for nonlinear systems * parametrization of conditioned invariant subspaces The book is an essential resource for all researchers and professionals in applied mathematics and control engineering who are
Review
"This volume contains lectures presented at the workshop 'Advances in Mathematical Systems Theory'.... Many of the contributors are leading international researchers in the field. The main topics are recent advances in nonlinear systems theory, including parameterization problems and behaviour of the linear system, convolution codes, complementary and hybrid systems. Controllability and stabilizability of infinite-dimensional systems are treated as well." --Applications of Mathematics
Synopsis
Written by leading researchers in the field, this self-contained volume surveys advances in mathematical systems theory and control. A cross-section of major research directions is addressed, including hybrid systems theory, robust control and stability of linear and nonlinear systems, parametrization of linear systems, and control of infinite dimensional systems. This will be a useful resource for professionals and researchers in systems and control theory.
Synopsis
This volume contains the lectures presented at the workshop on "Advances in Mathematical Systems Theory," held on the island of Borkum, Germany (April 20-23, 1999). The book will be of interest to graduate students and researchers interested in control theory and mathematical systems theory, who will find in-depth analysis and presentations from diverse perspectives interacting in this lively area. The editors are proud to dedicate this volume to Diederich Hinrichsen on the occasion of his 60th birthday in acknowl- edgment of his major contributions to linear systems theory and control theory and his long-term achievements in establishing mathematical sys- tems theory in Germany. We all owe much to him as a teacher, colleague, and friend. The editors thank the Graduiertenkolleg "Komplexe Dynamische Sys- teme" at the University of Bremen as well as the European "Nonlinear Control Network" for providing financial support that enabled this work- shop. Augsburg, Germany Fritz Colonius Wiirzburg, Germany Uwe Helmke Kaiserslautern, Germany Dieter Pratzel-Wolters Bremen, Germany Fabian Wirth Introduction The workshop "Advances in Mathematical Systems Theory" took place in honor of Diederich Hinrichsen on the occasion of his 60th birthday. The following chapters are based on invited lectures and cover a wide range of topics in linear and nonlinear systems theory including parameteriza- tion problems, behaviors of linear systems and convolutional codes, as well as complementarity systems and hybrid systems.
Table of Contents
Preface; Introduction; 1. Transitory Behavior of Uncertain Systems; 2. Robust Stability of Multivariate Polynomials; 3. Robustness of Nonlinear Systems and Their Domains of Attraction; 4. On Stability Radii of Slowly Time-Varying Systems; 5. An Invariance Radius for Nonlinear Systems; 6. State and Continuity; 7. On the Parametrization of Conditioned Invariant Subspaces; 8. Duality Between Multidimensional Convolutional Codes and Systems; 9. Control of Rate- Bounded Hybrid Systems with Liveness Constraints; 10. A General Principle of Marked Extraction; 11. Between Mathematical Programming and System Theory: Linear Complementarity Systems; 12. Exact Controllability of C(subscript-0)-groups with One-Dimensional Input Operators; 13. Normalized Co-prime Factorizations for Strongly Stabilizable Systems; 14. Low-Gain Integral Control of Infinite- Dimensional Regular Linear Systems Subject to Input Hysteresis; Index