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Prolongations and stability analysis via lyapunov functions of dynamical polysystems

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Abstract

The purpose of this paper is to explore asymptotic stability properties of dynamical polysystems in the vicinity of an arbitrary set by means of suitably defined Lyapunov functions. Both necessary and sufficient conditions are established using higher-order prolongations and transitizing extensions of the reachable map. For smooth systems in particular, the main sufficient conditions derived can be tested without prior knowledge of the system trajectories.

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Authors and Affiliations

  1. Department of Mathematics, National Technical University, Zografou Campus, 15773, Athens, Greece

    J. Tsinias

  2. Department of Physics, Division of Electronics, University of Athens TYPA, Panepistimioupoli, 15771, Athens, Greece

    N. Kalouptsidis

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  1. J. Tsinias
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  2. N. Kalouptsidis
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Tsinias, J., Kalouptsidis, N. Prolongations and stability analysis via lyapunov functions of dynamical polysystems. Math. Systems Theory 20, 215–233 (1987). https://doi.org/10.1007/BF01692066

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  • DOI: https://doi.org/10.1007/BF01692066

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