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An Overview of Finite-Time Stability

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Current Trends in Nonlinear Systems and Control

Part of the book series: Systems and Control: Foundations & Applications ((SCFA))

Summary

Finite-time stability (FTS) is a concept that was first introduced in the 1950s. The FTS concept differs from classical stability in two important ways. First, it deals with systems whose operation is limited to a fixed finite interval of time. Second, FTS requires prescribed bounds on system variables. For systems that are known to operate only over a finite interval of time and whenever, from practical considerations, the systems’ variables must lie within specific bounds, FTS is the only meaningful definition of stability. This overview will first present a short history of the development of the concept of FTS. Then it will present some important analysis and design results for linear, nonlinear, and stochastic systems. Finally some applications of the theory will be presented.

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Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, NM, 87131, USA

    Peter Dorato

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  1. Peter Dorato
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica Sistemi e Produzione, Università di Roma “Tor Vergata”, Via del Politecnico 1, I-00133, Roma, Italia

    Laura Menini  & Luca Zaccarian  & 

  2. Department of Electrical and Computer Engineering, University of New Mexico, EECE Building MSC01 1100, Albuquerque, NM, 87131-0001, USA

    Chaouki T. Abdallah

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Dorato, P. (2006). An Overview of Finite-Time Stability. In: Menini, L., Zaccarian, L., Abdallah, C.T. (eds) Current Trends in Nonlinear Systems and Control. Systems and Control: Foundations & Applications. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4470-9_10

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