Dynamical Systems: Stability, Controllability and Chaotic Behavior

Dynamical Systems: Stability, Controllability and Chaotic Behavior

Author: Stefan Pickl, Werner Krabs

Format: Hardcover

Pages: 238

ISBN: 9783642137211

Language: English

Publisher: Springer

Release Date: September 14, 2010

Description du Livre

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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