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Exponential Stability of Nonlinear Time-Varying Differential Equations and Partial Averaging

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Abstract.

In this paper we formulate, within the Liapunov framework, a sufficient condition for exponential stability of a differential equation. This condition gives rise to a new averaging result referred to as “partial averaging”: exponential stability of a system , with α sufficiently large, is implied by exponential stability of a time-varying system .

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Authors and Affiliations

  1. SYSTeMS, Universiteit Gent, Technologiepark-Zwijnaarde 9, 9052 Gent (Zwijnaarde), Belgium.¶Joan Peuteman is presently working at the KHBO, Departement Industrieële Wetenschappen en Technologie, Zeedijk 101, 8400 Oostende, Belgium. Joan.Peuteman@kh.khbo.be., , , , , , BE

    Joan Peuteman

  2. SYSTeMS, Universiteit Gent, Technologiepark-Zwijnaarde 9, 9052 Gent (Zwijnaarde), Belgium., , , , , , BE

    Dirk Aeyels

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  1. Joan Peuteman
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  2. Dirk Aeyels
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Date received: March 28, 2000. Date revised: March 7, 2001.

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Peuteman, J., Aeyels, D. Exponential Stability of Nonlinear Time-Varying Differential Equations and Partial Averaging. Math. Control Signals Systems 15, 42–70 (2002). https://doi.org/10.1007/s004980200002

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  • DOI: https://doi.org/10.1007/s004980200002

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