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Erschienen in:
General Theory Kapitel lesen Erstes Kapitel lesen

2013 | OriginalPaper | Buchkapitel

6. Linear Systems

verfasst von : Vladimir L. Kharitonov

Erschienen in: Time-Delay Systems

Verlag: Birkhäuser Boston

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Abstract

In this chapter we consider the class of neutral type linear systems with one delay. We define the fundamental matrix of such a system and present the Cauchy formula for the solution of an initial value problem. This formula is used to compute a quadratic functional with a given time derivative along the solutions of the time-delay system. It is demonstrated that this functional is defined by a special matrix valued function, which is called a Lyapunov matrix for a time-delay system. A thorough analysis of the basic properties of the matrix is included. Complete type functionals are introduced, and various applications of the functionals are discussed.

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Vorheriges Kapitel General Theory
Nächstes Kapitel Distributed Delay Case
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Metadaten
Titel
Linear Systems
verfasst von
Vladimir L. Kharitonov
Copyright-Jahr
2013
Verlag
Birkhäuser Boston
Buch
Time-Delay Systems

Print ISBN: 978-0-8176-8366-5

Electronic ISBN: 978-0-8176-8367-2

Copyright-Jahr: 2013

DOI
https://doi.org/10.1007/978-0-8176-8367-2_6

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