Fritz Colonius – författare

This new text/reference is an excellent resource for the foundations and applications of control theory and nonlinear dynamics. All graduates, practitioners, and professionals in control theory, dynamical systems, perturbation theory, engineering, physics and nonlinear dynamics will find the book a rich source of ideas, methods and applications. With its careful use of examples and detailed development, it is suitable for use as a self-study/reference guide for all scientists and engineers.

This self-contained volume surveys advances in mathematical systems theory and control. Fifteen chapters by leading researchers address cross-section of major research directions: hybrid systems theory, robust control and stability of linear and nonlinear systems, parametrization of linear systems and control of infinite dimensional systems. Professionals and researchers in systems and control engineering, applied mathematics, and systems engineering will find the book a useful resource.

This book provides an introduction to the interplay between linear algebra and dynamical systems in continuous time and in discrete time. It first reviews the autonomous case for one matrix A via induced dynamical systems in {R}^d and on Grassmannian manifolds. Then the main nonautonomous approaches are presented for which the time dependency of A(t) is given via skew-product flows using periodicity, or topological (chain recurrence) or ergodic properties (invariant measures). The authors develop generalizations of (real parts of) eigenvalues and eigenspaces as a starting point for a linear algebra for classes of time-varying linear systems, namely periodic, random, and perturbed (or controlled) systems.The book presents for the first time in one volume a unified approach via Lyapunov exponents to detailed proofs of Floquet theory, of the properties of the Morse spectrum, and of the multiplicative ergodic theorem for products of random matrices. The main tools, chain recurrence and Morse decompositions, as well as classical ergodic theory are introduced in a way that makes the entire material accessible for beginning graduate students.

This self-contained volume surveys advances in mathematical systems theory and control. Fifteen chapters by leading researchers address cross-section of major research directions: hybrid systems theory, robust control and stability of linear and nonlinear systems, parametrization of linear systems and control of infinite dimensional systems. Professionals and researchers in systems and control engineering, applied mathematics, and systems engineering will find the book a useful resource.

This new text/reference is an excellent resource for the foundations and applications of control theory and nonlinear dynamics. All graduates, practitioners, and professionals in control theory, dynamical systems, perturbation theory, engineering, physics and nonlinear dynamics will find the book a rich source of ideas, methods and applications. With its careful use of examples and detailed development, it is suitable for use as a self-study/reference guide for all scientists and engineers.

This self-contained volume surveys advances in mathematical systems theory and control. Fifteen chapters by leading researchers address cross-section of major research directions: hybrid systems theory, robust control and stability of linear and nonlinear systems, parametrization of linear systems and control of infinite dimensional systems. Professionals and researchers in systems and control engineering, applied mathematics, and systems engineering will find the book a useful resource.

This new text/reference is an excellent resource for the foundations and applications of control theory and nonlinear dynamics. All graduates, practitioners, and professionals in control theory, dynamical systems, perturbation theory, engineering, physics and nonlinear dynamics will find the book a rich source of ideas, methods and applications. With its careful use of examples and detailed development, it is suitable for use as a self-study/reference guide for all scientists and engineers.

This is the second volume of a three-volume treatise which presents the mathematical foundations of systems and control theory in a self-contained, comprehensive, detailed and mathematically rigorous way. The work combines the features of a detailed introductory textbook with those of a reference source.Volume II concentrates on problems of control, measurement and feedback control for time-varying and time-invariant linear systems. Special features are:• a comprehensive treatment of controllability and observability• an analysis of reachable sets under bounded controls with applications to the time-optimal control problem• a detailed construction of canonical forms for controllable systems under similarity transformations, including an application of these forms to the topological analysis of system spaces• a new module-theoretic approach to Rosenbrock systems in time domain• an introduction to balancing and model reduction by balanced truncation• an introduction to a general feedback control theory of input-output systems• a detailed treatment of stabilization and observation problems for time-invariant linear systems• a self-contained proof of Rosenbrock’s theorem by state space methods.Throughout the book there are many examples, figures and exercises illustrating the text which help bring out the intuitive ideas behind the mathematical constructions. The book should be accessible to mathematics students after two years of study and also to engineering students with a good mathematical background. It will be of value for researchers in systems theory as well as for mathematicians and engineers who wish to learn about the mathematical foundations of the above topics.

This is the second volume of a three-volume treatise which presents the mathematical foundations of systems and control theory in a self-contained, comprehensive, detailed and mathematically rigorous way. The work combines the features of a detailed introductory textbook with those of a reference source.Volume II concentrates on problems of control, measurement and feedback control for time-varying and time-invariant linear systems. Special features are:• a comprehensive treatment of controllability and observability• an analysis of reachable sets under bounded controls with applications to the time-optimal control problem• a detailed construction of canonical forms for controllable systems under similarity transformations, including an application of these forms to the topological analysis of system spaces• a new module-theoretic approach to Rosenbrock systems in time domain• an introduction to balancing and model reduction by balanced truncation• an introduction to a general feedback control theory of input-output systems• a detailed treatment of stabilization and observation problems for time-invariant linear systems• a self-contained proof of Rosenbrock’s theorem by state space methods.Throughout the book there are many examples, figures and exercises illustrating the text which help bring out the intuitive ideas behind the mathematical constructions. The book should be accessible to mathematics students after two years of study and also to engineering students with a good mathematical background. It will be of value for researchers in systems theory as well as for mathematicians and engineers who wish to learn about the mathematical foundations of the above topics.

This is the third and final volume of Mathematical Systems Theory. Like the preceding volumes, it presents the mathematical foundations of systems and control theory in a self-contained, comprehensive, detailed, and mathematically rigorous manner. The exposition proceeds from the very general to the more specific, with rigorous mathematics complemented by numerous illustrations and explanatory remarks.Volume III comprises two chapters and an appendix. In contrast to the first two volumes, only continuous-time systems are considered here. Chapter 9 addresses linear-quadratic optimal control and the Riccati equation, while Chapter 10 deals with zero dynamics and adaptive feedback regulation. Distinctive features include:• a comprehensive treatment of the linear-quadratic optimal control problem• a presentation of the bounded real and the Kalman–Yakubovich–Popov Lemma• a systematic development of spectral factorization• a study of the relative degree in state space and frequency domain• a detailed exposition of the Byrnes–Isidori form and zero dynamics• a development of the fundamentals of high-gain adaptive and funnel control.The book combines the characteristics of a detailed introductory textbook with those of a reference source. The material should be accessible to mathematics students after two years of study, as well as to engineering students with a strong mathematical background. It will be of value to researchers in systems theory, as well as to mathematicians and engineers seeking to acquire a solid understanding of the mathematical foundations of the topics outlined above.

This is the third and final volume of Mathematical Systems Theory. Like the preceding volumes, it presents the mathematical foundations of systems and control theory in a self-contained, comprehensive, detailed, and mathematically rigorous manner. The exposition proceeds from the very general to the more specific, with rigorous mathematics complemented by numerous illustrations and explanatory remarks.Volume III comprises two chapters and an appendix. In contrast to the first two volumes, only continuous-time systems are considered here. Chapter 9 addresses linear-quadratic optimal control and the Riccati equation, while Chapter 10 deals with zero dynamics and adaptive feedback regulation. Distinctive features include:• a comprehensive treatment of the linear-quadratic optimal control problem• a presentation of the bounded real and the Kalman–Yakubovich–Popov Lemma• a systematic development of spectral factorization• a study of the relative degree in state space and frequency domain• a detailed exposition of the Byrnes–Isidori form and zero dynamics• a development of the fundamentals of high-gain adaptive and funnel control.The book combines the characteristics of a detailed introductory textbook with those of a reference source. The material should be accessible to mathematics students after two years of study, as well as to engineering students with a strong mathematical background. It will be of value to researchers in systems theory, as well as to mathematicians and engineers seeking to acquire a solid understanding of the mathematical foundations of the topics outlined above.

This research monograph deals with optimal periodic control problems for systems governed by ordinary and functional differential equations of retarded type. Particular attention is given to the problem of local properness, i.e. whether system performance can be improved by introducing periodic motions. Using either Ekeland's Variational Principle or optimization theory in Banach spaces, necessary optimality conditions are proved. In particular, complete proofs of second-order conditions are included and the result is used for various versions of the optimal periodic control problem. Furthermore a scenario for local properness (related to Hopf bifurcation) is drawn up, giving hints as to where to look for optimal periodic solutions. The book provides mathematically rigorous proofs for results which are potentially of importance in chemical engineering and aerospace engineering.

This research monograph deals with optimal periodic control problems for systems governed by ordinary and functional differential equations of retarded type. Particular attention is given to the problem of local properness, i.e. whether system performance can be improved by introducing periodic motions. Using either Ekeland''s Variational Principle or optimization theory in Banach spaces, necessary optimality conditions are proved. In particular, complete proofs of second-order conditions are included and the result is used for various versions of the optimal periodic control problem. Furthermore a scenario for local properness (related to Hopf bifurcation) is drawn up, giving hints as to where to look for optimal periodic solutions. The book provides mathematically rigorous proofs for results which are potentially of importance in chemical engineering and aerospace engineering.

This volume originates from the Third Nonlinear Control Workshop "- namics, Bifurcations and Control", held in Kloster Irsee, April 1-3 2001. As the preceding workshops held in Paris (2000) and in Ghent (1999), it was organized within the framework of Nonlinear Control Network funded by the European Union (http://www.supelec.fr/lss/NCN). The papers in this volume center around those control problems where phenomena and methods from dynamical systems theory play a dominant role. Despite the large variety of techniques and methods present in the c- tributions, a rough subdivision can be given into three areas: Bifurcation problems, stabilization and robustness, and global dynamics of control s- tems. A large part of the fascination in nonlinear control stems from the fact that is deeply rooted in engineering and mathematics alike. The contributions to this volume reflect this double nature of nonlinear control. We would like to take this opportunity to thank all the contributors and the referees for their careful work. Furthermore, it is our pleasure to thank Franchise Lamnabhi-Lagarrigue, the coordinator of our network, for her s- port in organizing the workshop and the proceedings and for the tremendous efforts she puts into this network bringing the cooperation between the d- ferent groups to a new level. In particular, the exchange and the active p- ticipation of young scientists, also reflected in the Pedagogical Schools within the Network, is an asset for the field of nonlinear control.

This volume originates from the Third Nonlinear Control Workshop "- namics, Bifurcations and Control", held in Kloster Irsee, April 1-3 2001. As the preceding workshops held in Paris (2000) and in Ghent (1999), it was organized within the framework of Nonlinear Control Network funded by the European Union (http://www.supelec.fr/lss/NCN). The papers in this volume center around those control problems where phenomena and methods from dynamical systems theory play a dominant role. Despite the large variety of techniques and methods present in the c- tributions, a rough subdivision can be given into three areas: Bifurcation problems, stabilization and robustness, and global dynamics of control s- tems. A large part of the fascination in nonlinear control stems from the fact that is deeply rooted in engineering and mathematics alike. The contributions to this volume reflect this double nature of nonlinear control. We would like to take this opportunity to thank all the contributors and the referees for their careful work. Furthermore, it is our pleasure to thank Franchise Lamnabhi-Lagarrigue, the coordinator of our network, for her s- port in organizing the workshop and the proceedings and for the tremendous efforts she puts into this network bringing the cooperation between the d- ferent groups to a new level. In particular, the exchange and the active p- ticipation of young scientists, also reflected in the Pedagogical Schools within the Network, is an asset for the field of nonlinear control.