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.

Autorentext

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.

Inhalt
1 Introduction.- 2 Dynamics, Perturbations, and Control.- 2.1 Perturbations of Complex behavior.- 2.2 Approximation of Complex Systems.- 2.3 Generic Behavior of Perturbations.- 2.4 Stability Boundaries and Multistability.- 2.5 Reachability in Control Systems.- 2.6 Linear and Nonlinear Stability Radii.- 2.7 Stabilization of Bilinear Systems.- 2.8 The Lyapunov Spectrum of Matrices.- I Global Theory.- 3 Control Sets.- 4 Control Flows and Limit behavior.- II Linearization Theory.- 5 Linear Flows on Vector Bundles.- 6 Bilinear Systems on Vector Bundles.- 7 Linearization at a Singular Point.- III Applications.- 8 One-Dimensional Control Systems.- 9 Examples for Global behavior.- 10 Examples for the Spectrum.- 11 Stability Radii and Robust Stability.- 12 Open and Closed Loop Stabilization.- 13 Dynamics of Perturbations.- IV Appendices.- A Geometric Control Theory.- A.1 Differentiable Manifolds and Vector Fields.- A.2 Basic Definitions for Control Systems.- A.3 The Orbit Theorem.- A.4 Local Accessibility.- A.5 Notes.- B Dynamical Systems.- B.1 Vector Bundles.- B.2 Morse Decompositions, Attractors, Chains.- B.3 Ergodic Theory.- B.4 Notes.- C Numerical Computation of Orbits.- C.1 Orbits and Approximately Invariant Sets.- C.2 Computing Approximately Invariant Sets.- C.3 Computation via Time Optimal Control.- C.4 Notes.- D.1 Problem Formulation and Main Results.- D.2 Discounted and Average Functional.- D.3 Approximation of the Spectrum.- D.4 The Hamilton-Jacobi-Bellman Equation.- D.5 Discounted Optimal Control Problems.- D.6 Notes.