Stability of Dynamical Systems

By

  • Xiaoxin Liao, Huazhong University of Science and Technology, Wuhan, China
  • L.Q. Wang, The University of Hong Kong, Hong Kong
  • P. Yu, The University of Western Ontario, London, Ontario, Canada

The main purpose of developing stability theory is to examine dynamic responses of a system to disturbances as the time approaches infinity. It has been and still is the object of intense investigations due to its intrinsic interest and its relevance to all practical systems in engineering, finance, natural science and social science. This monograph provides some state-of-the-art expositions of major advances in fundamental stability theories and methods for dynamic systems of ODE and DDE types and in limit cycle, normal form and Hopf bifurcation control of nonlinear dynamic systems.
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Audience

Graduate students in applied mathematics, mechanics, control theory, theoretical physics, mathematical biology, information theory, and scientific computation; Comprehensive handbook of stability theory for practicing aerospace, control, mechanical, structural, naval and civil engineers

 

Book information

  • Published: August 2007
  • Imprint: ELSEVIER
  • ISBN: 978-0-444-53110-0


Table of Contents

PrefaceChapter 1. Fundamental Concepts and Mathematical ToolsChapter 2. Linear Systems with Constant CoefficientsChapter 3. Time-Varying Linear SystemsChapter 4. Lyapunov Direct MethodChapter 5. Development of Lyapunov Direct MethodChapter 6. Nonlinear Systems with Separate VariablesChapter 7. Iteration Method for StabilityChapter 8. Dynamical Systems with Time DelayChapter 9. Absolute Stability of Nonlinear Control SystemsChapter 10. Stability of Neural NetworksChapter 11. Limit Cycle, Normal Form and Hopf Bifurcation Control