Abstract
The dynamical theory of control uses concepts and ideas from dynamical systems theory to study nonlinear control systems. In this context the basic control theoretic notions are control sets, chain control sets, and the spectrum. They are based on the dynamical systems concepts of transitivity, chain recurrence, and Lyapunov exponents for the associated control flow. Together they allow an analysis of the local and global fine structure of control systems, such as controllability regions and their domains of attraction, robust stability and stability radii, and open and closed loop stabilization. Various examples illustrating the use of a dynamical theory of control were presented in Chapters 8 to 12.
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