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The aim of Stability of Finite and Infinite Dimensional Systems is to provide new tools for specialists in control system theory, stability theory of ordinary and partial differential equations, and differential-delay equations.
Stability of Finite and Infinite Dimensional Systems is the first book that gives a systematic exposition of the approach to stability analysis which is based on estimates for matrix-valued and operator-valued functions, allowing us to investigate various classes of finite and infinite dimensional systems from the unified viewpoint. This book contains solutions to the problems connected with the Aizerman and generalized Aizerman conjectures and presents fundamental results by A. Yu. Levin for the stability of nonautonomous systems having variable real characteristic roots.
Stability of Finite and Infinite Dimensional Systems is intended not only for specialists in stability theory, but for anyone interested in various applications who has had at least a first-year graduate-level course in analysis.
List of contents
I. Preliminaries.- 2. Estimates for Matrix-Valued Functions.- 3. Linear Finite Dimensional Systems.- 4. Linear Finite Dimensional Systems (Continuation).- 5. Nonlinear Finite Dimensional Systems With Autonomous Linear Parts.- 6. Nonlinear Finite Dimensional Systems with Time-Variant Linear Parts.- 7. Essentially Nonlinear Finite Dimensional Systems.- 8. Linear Autonomous Systems with Delay.- 9. Linear Time-Variant Systems with Delay.- 10. NONLINEAR SYSTEMS WITH DELAY.- 11. Linear Neutral Type Systems.- 12. Nonlinear Neutral Type Functional Differential Systems.- 13. Strongly Continuous Semigroups.- 14. Linear Time-Variant Equations in Banach Spaces.- 15. Semilinear Equations in Banach Spaces with Constant Linear Parts.- 16. Semilinear Equations in Banach Spaces with Time-Variant Linear Parts.- 17. Appendix.- List of Main Symbols.
