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Further results on Lyapunov functions for slowly time-varying systems

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Abstract

We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily exponentially stable. This complements our previous Lyapunov function constructions for rapidly time-varying dynamics. We also explicitly construct input-to-state stable Lyapunov functions for slowly time-varying control systems. We illustrate our findings by constructing explicit Lyapunov functions for a pendulum model, an example from identification theory, and a perturbed friction model.

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Authors and Affiliations

  1. UMR Analyse des Systèmes et Biométrie INRA, 2, pl. Viala, 34060, Montpellier, France

    Frédéric Mazenc

  2. Department of Mathematics, Louisiana State University, Baton Rouge, LA, 70803-4918, USA

    Michael Malisoff

Authors
  1. Frédéric Mazenc
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  2. Michael Malisoff
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Correspondence to Michael Malisoff.

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Mazenc, F., Malisoff, M. Further results on Lyapunov functions for slowly time-varying systems. Math. Control Signals Syst. 19, 1–21 (2007). https://doi.org/10.1007/s00498-006-0010-4

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  • DOI: https://doi.org/10.1007/s00498-006-0010-4

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