Souza Josiney A. The Dynamic Morse Theory of Control Systems

Cambridge Scholars Publishing, 2020. — 342 p. — ISBN 978-1-5275-4507-6.This book provides insights into the dynamics of control systems with the integration of conceptions such as stability, controllability, attraction, and chain transitivity. It highlights the importance of Morse theory with its feature of describing the global dynamics of systems, presented here for the first time in control theory. The mathematical formulations are comprehensive, designed especially for students, researches, and professionals interested in qualitative studies of control systems. The reader will find the book an accessible source of basic definitions, properties, methods, examples, theorems, references, lists of problems, and open questions. Parts of the book may be used for courses or seminars in mathematics or control-theoretic engineering, and its reference guide will serve as a great resource for research projects and academic dissertations on control theory or dynamical systems.Fundamental Theory of Control systems
Elementary Concepts
Minimal sets and transitivity
Limit sets and prolongations
Asymptotic transitivity
Attractors and repellers
Chain transitivity
Morse decompositions
Dynamical systems
Differentiable manifolds