Advances In Mathematical Systems Theory: A Volume In Honor Of Diederich Hinrichsen (systems & Control: Foundations & Applications)

"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** 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 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

Front Matter....Pages i-xxx Transitory Behavior of Uncertain Systems....Pages 1-17 Robust Stability of Multivariate Polynomials....Pages 19-29 Robustness of Nonlinear Systems and Their Domains of Attraction....Pages 31-54 On Stability Radii of Slowly Time-Varying Systems....Pages 55-75 An Invariance Radius for Nonlinear Systems....Pages 77-91 State and Continuity....Pages 93-102 Parameterization of Conditioned Invariant Subspaces....Pages 103-133 Duality Between Multidimensional Convolutional Codes and Systems....Pages 135-150 Control of Rate-Bounded Hybrid Systems with Liveness Constraints....Pages 151-168 A General Principle of Marked Extraction....Pages 169-183 Between Mathematical Programming and Systems Theory: Linear Complementarity Systems....Pages 185-219 Exact Controllability of C 0 -groups with One-Dimensional Input Operators....Pages 221-242 Normalized Coprime Factorizations for Strongly Stabilizable Systems....Pages 243-254 Low-Gain Integral Control of Infinite-Dimensional Regular Linear Systems Subject to Input Hysteresis....Pages 255-293 Back Matter....Pages 294-299