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This book presents a modern and self-contained treatment of the Liapunov method for stability analysis, in the framework of mathematical nonlinear control theory. A Particular focus is on the problem of the existence of Liapunov functions (converse Liapunov theorems) and their regularity, whose interest is especially motivated by applications to automatic control. Many recent results in this area have been collected and presented in a systematic way. Some of them are given in extended, unified versions and with new, simpler proofs. In the 2nd edition of this successful book several new sections were added and old sections have been improved, e.g about the Zubovs method, Liapunov functions for discontinuous systems and cascaded systems. Many new examples, explanations and figures were added making this book accessible and well readable for engineers as well as mathematicians.

Control theory. --- Lyapunov functions. --- Stability. --- Dynamics --- Mechanics --- Motion --- Vibration --- Benjamin-Feir instability --- Equilibrium --- Functions, Liapunov --- Liapunov functions --- Differential equations --- Machine theory --- System theory. --- Vibration. --- Statistical physics. --- Control, Robotics, Mechatronics. --- Systems Theory, Control. --- Complex Systems. --- Vibration, Dynamical Systems, Control. --- Statistical Physics and Dynamical Systems. --- Physics --- Mathematical statistics --- Cycles --- Sound --- Systems, Theory of --- Systems science --- Science --- Statistical methods --- Philosophy --- Systems theory. --- Control engineering. --- Robotics. --- Mechatronics. --- Dynamical systems. --- Dynamics. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Statics --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Automation --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Programmable controllers

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This book offers a complete and detailed introduction to the theory of discrete dynamical systems, with special attention to stability of fixed points and periodic orbits. It provides a solid mathematical background and the essential basic knowledge for further developments such as, for instance, deterministic chaos theory, for which many other references are available (but sometimes, without an exhaustive presentation of preliminary notions). Readers will find a discussion of topics sometimes neglected in the research literature, such as a comparison between different predictions achievable by the discrete time model and the continuous time model of the same application. Another novel aspect of this book is an accurate analysis of the way a fixed point may lose stability, introducing and comparing several notions of instability: simple instability, repulsivity, and complete instability. To help the reader and to show the flexibility and potentiality of the discrete approach to dynamics, many examples, numerical simulations, and figures have been included. The book is used as a reference material for courses at a doctoral or upper undergraduate level in mathematics and theoretical engineering.

Dynamics. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Mathematics. --- Math --- Science

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• Reference Manager
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This book presents a modern and self-contained treatment of the Liapunov method for stability analysis, in the framework of mathematical nonlinear control theory. A Particular focus is on the problem of the existence of Liapunov functions (converse Liapunov theorems) and their regularity, whose interest is especially motivated by applications to automatic control. Many recent results in this area have been collected and presented in a systematic way. Some of them are given in extended, unified versions and with new, simpler proofs. In the 2nd edition of this successful book several new sections were added and old sections have been improved, e.g about the Zubovs method, Liapunov functions for discontinuous systems and cascaded systems. Many new examples, explanations and figures were added making this book accessible and well readable for engineers as well as mathematicians.

Classical mechanics. Field theory --- Applied physical engineering --- Engineering sciences. Technology --- Computer science --- neuronale netwerken --- procesautomatisering --- systeemtheorie --- systeembeheer --- dynamica --- regeltechniek