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Dynamical Systems - Stability, Controllability and Chaotic Behavior (Hardcover, 2010 ed.)
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Dynamical Systems - Stability, Controllability and Chaotic Behavior (Hardcover, 2010 ed.)
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At the end of the nineteenth century Lyapunov and Poincare
developed the so called qualitative theory of differential
equations and introduced geometric- topological considerations
which have led to the concept of dynamical systems. In its present
abstract form this concept goes back to G.D. Birkhoff. This is also
the starting point of Chapter 1 of this book in which uncontrolled
and controlled time-continuous and time-discrete systems are
investigated. Controlled dynamical systems could be considered as
dynamical systems in the strong sense, if the controls were
incorporated into the state space. We, however, adapt the
conventional treatment of controlled systems as in control theory.
We are mainly interested in the question of controllability of
dynamical systems into equilibrium states. In the non-autonomous
time-discrete case we also consider the problem of stabilization.
We conclude with chaotic behavior of autonomous time discrete
systems and actual real-world applications.
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