Advances in Mathematical Systems Theory A Volume in Honor of Diederich Hinrichsen

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 TOC: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

1 Transitory Behavior of Uncertain Systems.- 1.1 Introduction.- 1.2 Transient Excursions.- 1.3 Pseudospectra and Spectral Value Sets.- 1.4 State Feedback.- 1.5 Transient Excursions of Uncertain Systems.- 2 Robust Stability of Multivariate Polynomials.- 2.1 Introduction.- 2.2 Basic Notions and Definitions.- 2.2.1 Classes of Stable Polynomials.- 2.3 Properties of Stable Polynomials.- 2.4 Zero Exclusion Principle.- 3 Robustness of Nonlinear Systems and Their Domains of Attraction.- 3.1 Introduction.- 3.2 Preliminaries.- 3.3 Linearization Theory.- 3.4 Calculating the Local Stability Radius.- 3.5 Robust Domains of Attraction.- 3.6 An Optimal Control Characterization of the Robust Domain of Attraction.- 3.7 Conclusion.- 4 On Stability Radii of Slowly Time-Varying Systems.- 4.1 Introduction.- 4.2 Perturbation Classes.- 4.3 Stability of Nonlinearly Perturbed Linear Systems.- 4.4 Stability Radii of Slowly Time-Varying Systems.- 4.5 Two Lemmas.- 4.6 Conclusions.- 5 An Invariance Radius for Nonlinear Systems.- 5.1 Introduction.- 5.2 Background on Invariant Control Sets and Chain Control Sets.- 5.3 An Invariance Radius for Nonlinear Systems.- 6 State and Continuity.- 6.1 Introduction.- 6.2 Linear Differential Systems.- 6.3 Latent Variables.- 6.4 State Representations.- 6.5 Smoothing Functionals.- 6.6 Main Results.- 6.7 Proofs.- 6.8 Remarks.- 7 Parameterization of Conditioned Invariant Subspaces.- 7.1 Introduction.- 7.2 Preliminaries.- 7.3 On Conditioned Invariant Subspaces.- 7.4 The State Space Approach.- 7.5 On the Parameterization of Conditioned Invariant Subspaces.- 7.6 Topology of Tight Conditioned Invariant Subspaces.- 7.7 Brunovsky Strata for Conditioned Invariant Subspaces...- 8 Duality Between Multidimensional Convolutional Codes and Systems.- 8.1 Introduction.- 8.2 Multidimensional Convolutional Codes.- 8.3 Duality Between Codes and Behaviors.- 8.4 First-Order Representations for One-Dimensional Codes.- 8.5 Conclusion.- 9 Control of Rate-Bounded Hybrid Systems with Liveness Constraints.- 9.1 Introduction.- 9.2 Hybrid Machines.- 9.3 Liveness.- 9.4 Control.- 10 A General Principle of Marked Extraction.- 10.1 Introduction.- 10.2 Joint Production and the Substitution Theorem.- 10.3 Marked Extraction in Convex Sets.- 10.4 The Factorial Complex of a Krull Monoid.- 11 Between Mathematical Programming and Systems Theory: Linear Complementarity Systems.- 11.1 Introduction.- 11.2 Examples.- 11.3 Existence and uniqueness of solutions.- 11.4 Linear complementarity systems.- 11.5 A distributional interpretation.- 11.6 Well-posedness.- 11.7 Relay systems.- 11.8 Discontinuous dependence on initial conditions.- 11.9 Conclusions.- 12 Exact Controllability of Co-groups with One-Dimensional Input Operators.- 12.1 Introduction.- 12.2 System Description.- 12.3 Exact Controllability.- 12.4 Proofs of the Main Results.- 12.5 An Example.- 13 Normalized Coprime Factorizations for Strongly Stabilizable Systems.- 13.1 Introduction.- 13.2 Problem Formulation and Mathematical Background.- 13.3 Formulae for Normalized Coprime Factorizations.- 13.4 Application to Hybrid Flexible Structures.- 14 Low-Gain Integral Control of Infinite-Dimensional Regular Linear Systems Subject to Input Hysteresis.- 14.1 Introduction.- 14.2 Preliminaries on Regular Linear Systems.- 14.3 A Class of Causal Monotone Nonlinear Operators.- 14.4 Integral Control in the Presence of Input Nonlinearities Satisfying (N1) to (N8).- 14.5 Hysteresis Nonlinearities Satisfying (N1) to (N8).- 14.6 Example: Controlled Diffusion Process with Output Delay.- 14.7 Appendix.