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Asymptotic stability for time-variant systems and observability: Uniform and nonuniform criteria

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Abstract

This paper presents some new criteria for uniform and nonuniform asymptotic stability of equilibria for time-variant differential equations and this within a Lyapunov approach. The stability criteria are formulated in terms of certain observability conditions with the output derived from the Lyapunov function. For some classes of systems, this system theoretic interpretation proves to be fruitful since—after establishing the invariance of observability under output injection—this enables us to check the stability criteria on a simpler system. This procedure is illustrated for some classical examples.

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Authors and Affiliations

  1. SYSTeMS, Universiteit Gent, Technologiepark-Zwijnaarde 9, 9052, Gent, Belgium

    D. Aeyels

  2. Institut Montefiore, B28, Université de Liège, 4000, Liège Sart-Tilman, Belgium

    R. Sepulchre & J. Peuteman

Authors
  1. D. Aeyels
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  2. R. Sepulchre
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  3. J. Peuteman
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Correspondence to D. Aeyels.

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This paper presents research results of the Belgian Programme on Interuniversity Poles of Attraction, initiated by the Belgian State, Prime Minister’s Office for Science, Technology, and Culture. The scientific responsibilty rests with its authors.

Work performed while at the Center for Systems Engineering and Applied Mechanics, Université Catholique de Louvain, Bâtiment Euler, 4–6 Avenue Georges Lemaître, 1348 Louvain-la-Neuve, Belgium.

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Aeyels, D., Sepulchre, R. & Peuteman, J. Asymptotic stability for time-variant systems and observability: Uniform and nonuniform criteria. Math. Control Signal Systems 11, 1–27 (1998). https://doi.org/10.1007/BF02741883

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