Global Attractors of Non-Autonomous Dynamical and Control Systems

Nonfiction, Science & Nature, Mathematics, Differential Equations, Technology, Electricity

• Author: David N Cheban
• ISBN: 9789814619844
• Publisher: World Scientific Publishing Company
• Publication: December 15, 2014
• Imprint: WSPC
• Language: English

The study of attractors of dynamical systems occupies an important position in the modern qualitative theory of differential equations. This engaging volume presents an authoritative overview of both autonomous and non-autonomous dynamical systems, including the global compact attractor. From an in-depth introduction to the different types of dissipativity and attraction, the book takes a comprehensive look at the connections between them, and critically discusses applications of general results to different classes of differential equations.

The new Chapters 15–17 added to this edition include some results concerning Control Dynamical Systems — the global attractors, asymptotic stability of switched systems, absolute asymptotic stability of differential/difference equations and inclusions — published in the works of author in recent years.

Contents:

• Stability of Autonomous Dynamical Systems
• Non-Autonomous Dissipative Dynamical Systems
• Analytic Dissipative Systems
• The Structure of the Levinson Center of System with the Condition of the Hyperbolicity
• Method of Lyapunov Functions
• Dissipativity of Some Classes of Equations
• Upper Semi-Continuity of Attractors
• The Relationship Between Pullback, Forward and Global Attractors
• Pullback Attractors of ℂ-Analytic Systems
• Pullback Attractors Under Discretization
• Global Attractors of Non-Autonomous Navier–Stokes Equations
• Global Attractors of V-Monotone Dynamical Systems
• Linear Almost Periodic Dynamical Systems
• Triangular Maps
• Compact Global Attractors of Control Systems
• Asymptotic Stability of Switched Systems
• Absolute Asymptotic Stability of Differential (Difference) Equations and Inclusions

Readership: This book is intended for mathematicians (scientists and university professors) who are working in the field of differential/difference equations, dynamical systems and control theory. It would also be useful for the graduate and post-graduate students who are interested in the theory of dynamical and control systems and their applications.
Key Features:

• This book is a unique book dedicated to the study of asymptotical behavior of nonautonomous dynamical systems and applications
• The new edition includes the important results obtained in the last ten years about Control Systems (global attractors, asymptotic stability of switched systems, absolute asymptotic stability)
• The new results (Chapters 15–17) added in the second edition belong to author