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.

Gives an approach based on estimates for matrix-valued functions which allows the investigation of various classes of equations from a unified viewpoint Provides the reader with a solution of the generalized Aizerman problem for NDEs Explains to the reader the generalized Bohl-Perron principle for neutral type systems and its integral version Gives explicit stability conditions for semilinear equations with linear neutral type parts and nonlinear causal mappings Includes supplementary material: sn.pub/extras

Inhalt

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.