Stability of Neutral Functional Differential Equations

In this monograph the author presents explicit conditions for the exponential, absolute and input-to-state stabilities including solution estimates of certain types of functional differential equations.
The main methodology used is based on a combination of recent norm estimates for matrix-valued functions, comprising the generalized Bohl-Perron principle, together with its integral version and the positivity of fundamental solutions.
A significant part of the book is especially devoted to the solution of the generalized Aizerman problem.

List of contents

Preliminaries.- Eigenvalues and Functions of Matrices.- Difference Equations with Continuous Time.- Linear Differential Delay Equations.- Linear Autonomous NDEs.- Linear Time-variant NDEs.- Nonlinear Vector NDEs.- Absolute Stability of Scalar NDEs.- Bounds for Characteristic Values of NDEs.

Summary

In this monograph the author presents explicit conditions for the exponential, absolute and input-to-state stabilities including solution estimates of certain types of functional differential equations.
The main methodology used is based on a combination of recent norm estimates for matrix-valued functions, comprising the generalized Bohl-Perron principle, together with its integral version and the positivity of fundamental solutions.
A significant part of the book is especially devoted to the solution of the generalized Aizerman problem.

Product details

• Authors: Michael Gil', Michael I Gil', Michael I. Gil'
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 01.01.2014
• EAN: 9789462390904
• ISBN: 978-94-62-39090-4
• No. of pages: 304
• Dimensions: 162 mm x 242 mm x 21 mm
• Weight: 590 g
• Illustrations: XIII, 304 p.
• Series: Atlantis Studies in Differential Equations; Atlantis Press; Atlantis Press; Atlantis Studies in Differential Equations
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Analysis