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General Theory

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Book cover Time-Delay Systems

Part of the book series: Control Engineering ((CONTRENGIN))

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Abstract

This chapter serves as a brief introduction to the theory of the retarded type time-delay system. It starts with a discussion of such basic notions as solutions, initial conditions, and the state of a time-delay system. Then some results on the existence and uniqueness of an initial value problem are presented. Continuity properties of the solutions are discussed as well. The main part of the chapter is devoted to stability analysis. Here we define concepts of stability, asymptotic stability, and exponential stability of the trivial solution of a time-delay system. Classical stability results, obtained using the Lyapunov–Krasovskii approach, are given in the form of necessary and sufficient conditions. A short section with historical comments concludes the chapter.

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Authors and Affiliations

  1. Faculty of Applied Mathematics and Processes of Control, Saint Petersburg State University, Saint Petersburg, Russia

    Vladimir L. Kharitonov

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  1. Vladimir L. Kharitonov
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Kharitonov, V.L. (2013). General Theory. In: Time-Delay Systems. Control Engineering. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8367-2_1

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  • DOI: https://doi.org/10.1007/978-0-8176-8367-2_1

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  • Print ISBN: 978-0-8176-8366-5

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