Geodesic
On the Lyapunov theorem for semi-dynamical systems
Trudy Instituta matematiki, Tome 29 (2021) no. 1, pp. 94-105

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The paper deals with the stability problem of semi-dynamical systems on an arbitrary metric space. Variants of theorems of Lyapunov's second method are presented in the form of sufficient conditions for non-asymptotic stability of compact positively invariant sets in the class of constant-sign auxiliary functions. A comparative analysis of the results of the second Lyapunov method is given, depending on the requirements regarding the zero-level set of Lyapunov functions. The relative non-asymptotic stability is studied when the Lyapunov function's zero level set consists of fixed points of the system. Illustrative examples are given. 
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     author = {B. S. Kalitine},
     title = {On the {Lyapunov} theorem for semi-dynamical systems},
     journal = {Trudy Instituta matematiki},
     pages = {94--105},
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     volume = {29},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2021_29_1_a8/}
}
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B. S. Kalitine. On the Lyapunov theorem for semi-dynamical systems. Trudy Instituta matematiki, Tome 29 (2021) no. 1, pp. 94-105. http://geodesic.mathdoc.fr/item/TIMB_2021_29_1_a8/