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Lyapunov-Krasovskii Functional Approach for Coupled Differential-Difference Equations with Multiple Delays

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Delay Differential Equations

Abstract

Coupled differential-difference equations (coupled DDEs) represent a very general class of time-delay systems. Indeed, traditional DDEs of retarded or neutral type, as well as singular systems, can all be considered as special cases of coupled DDEs. The coupled DDE formulation is especially effective when a system has a large number of state variables, but only a few of them involve time delays. In this chapter, the stability of such systems is studied by using a Lyapunov-Krasovskii functional method. For linear systems, a quadratic Lyapunov-Krasovskii functional is discretized to reduce the stability problem to a set of linear matrix inequalities for which effective numerical algorithms are available, and widely implemented in such software packages as MATLAB.

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Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, School of Engineering, Southern Illinois University, Edwardsville, IL, 62026-1805

    Keqin Gu

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  1. Hongfei Li
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Correspondence to Keqin Gu .

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Li, H., Gu, K. (2009). Lyapunov-Krasovskii Functional Approach for Coupled Differential-Difference Equations with Multiple Delays. In: Delay Differential Equations. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-85595-0_1

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  • DOI: https://doi.org/10.1007/978-0-387-85595-0_1

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  • Online ISBN: 978-0-387-85595-0

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