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Introduction to Time-Delay Systems

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Linear Parameter-Varying and Time-Delay Systems

Part of the book series: Advances in Delays and Dynamics ((ADVSDD,volume 3))

Abstract

The goal of this chapter is to introduce the main manners for representing time-delay systems. As for parameters in LPV systems, delays can also be classified in different categories depending on the their nature and the way they act on the system. Several real world examples are given to motivate the usefulness and relevance of time-delay systems in science and engineering. We notably discuss about the harmful and beneficial effects of the delays on the stability properties of dynamical systems. Controllers and observers that are specific to time-delay systems are finally briefly presented.

Nous pouvons rêver d’équations fonctionelles plus compliquées que les équations classiques parce qu’elles renfermeront en outre des intégrales prises entre le temps passé très éloigné et le temps actuel, qui apporteront la part de l’hérédité. (We may dream about more complicated functional equations than classical equations since they shall in addition contain integrals taken between the distant past time and the current time, which shall bring the share of heredity.)

Emile Picard

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Notes

  1. 1.

    The definition of the congestion window size may differ from one protocol to another.

  2. 2.

    More information on NS-2 available here http://nsnam.isi.edu/nsnam/index.php/Main_Page.

  3. 3.

    FIFO stands for “First-In-First-Out” and means that the packets leave the queue in the same order they entered. This is an order preserving queue.

  4. 4.

    See e.g. [223–225] for discrete-time switched systems and time-delay systems. These references do not consider delay-scheduled controllers.

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Briat, C. (2015). Introduction to Time-Delay Systems. In: Linear Parameter-Varying and Time-Delay Systems. Advances in Delays and Dynamics, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44050-6_4

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