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Impulsive Systems on Hybrid Time Domains

Part of the book series: IFSR International Series in Systems Science and Systems Engineering ((IFSR,volume 33))

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Abstract

Impulsive systems (systems of impulsive differential equations) model real world processes that undergo abrupt changes (impulses) in the state at a sequence of discrete times. These abrupt changes in systems’ states inspire the impulsive control mechanism. The theory of impulsive differential equations and its applications to impulsive control problems has been an active research area since 1990s. On the other hand, time-delay systems have been intensively studied in the past decades, mainly due to the ubiquity of time delays in physical processes such as proliferation process for solid avascular tumour, scattering process, milling process, and temperature control. Stability is one of the fundamental issues in system design, analysis and control. Recently, impulsive control has been shown to be a powerful approach to stabilize time-delay systems, and various stability and stabilization results have been obtained for impulsive time-delay systems.

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  1. Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada

    Xinzhi Liu & Kexue Zhang

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  1. Xinzhi Liu
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Liu, X., Zhang, K. (2019). Introduction. In: Impulsive Systems on Hybrid Time Domains. IFSR International Series in Systems Science and Systems Engineering, vol 33. Springer, Cham. https://doi.org/10.1007/978-3-030-06212-5_1

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