Abstract
In contrast to the case of a single dynamical system, the asymptotic stability of orbits of control systems cannot be characterized in terms of suitably defined Lyapunov functions. It is shown that the existence of Lyapunov functions corresponds to a stronger type of asymptotic stability, which is defined by introducing higher prolongations.
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References
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Kalouptsidis, N. Prolongations and Lyapunov functions in control systems. Math. Systems Theory 16, 233–249 (1983). https://doi.org/10.1007/BF01744578
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DOI: https://doi.org/10.1007/BF01744578