Mathematical Systems Theory II : Control, Observation, Realization, and Feedback

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.

Diederich Hinrichsen is a retired Professor of Mathematical Systems Theory at the University of Bremen.

Anthony J. Pritchard († 2007) was Professor of Mathematics and founder and director of the Control Theory Centre at the University of Warwick.

Fritz Colonius is a retired Professor of Applied Mathematics at the University of Augsburg. His main research interest is the interplay of control theory and dynamical systems theory.

Tobias Damm is Professor for Systems and Control Theory at RPTU University Kaiserslautern-Landau. His research interests include linear algebra and numerical analysis and the application of these to control theory.

Achim Ilchmann held a chair in Applied Mathematics at the Technical University of Ilmenau until his retirement in 2022. His research interests include the algebraic theory of time-varying linear systems, adaptive control, and Baroque architecture.

Birgit Jacob has been with the University of Wuppertal, Germany, since 2010, where she is a full professor in analysis. Her current research interests include the area of infinite-dimensional systems and operator theory, particularly well-posed linear systems and port-Hamiltonian systems.

Fabian R. Wirth is Professor for Dynamical Systems at the University of Passau. His research interests include stability theory, switched systems, infinite-dimensional and large-scale systems.