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Stability of Neutral Functional Differential Equations electronic resource by Michael I. Gil'.

By: Gil', Michael I [author.]Contributor(s): SpringerLink (Online service)Material type: TextTextSeries: Atlantis Studies in Differential EquationsPublication details: Paris : Atlantis Press : Imprint: Atlantis Press, 2014Description: XIII, 304 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9789462390911Subject(s): mathematics | Matrix theory | Functional equations | Systems theory | Mathematics | Difference and Functional Equations | Systems Theory, Control | Linear and Multilinear Algebras, Matrix TheoryDDC classification: 515.625 | 515.75 LOC classification: QA431Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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.
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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.

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.

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