Geodesic
Stability of Multi-Dimensional Discrete Systems With Varying Structure
International Journal of Applied Mathematics and Computer Science, Tome 9 (1999) no. 4, pp. 789-799.

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A new class of multi-dimensional discrete systems with varying structureis introduced. The notions of total solvability, p_t-boundedness, p_t-stability and asymptotic stability are defined. For studying properties of the solutions for the considered systems a curvilinear composition of mappings along discrete curves is used. Total solvability conditions similar to the Frobenius ones are obtained. Sufficient conditions for p_t-stability and asymptotic stability based on the Lyapunov functional method are also established. A two-dimensional system of Volterra equations is presented as an example of equations with varying structure.
Keywords: multi-dimensional systems, total solvability, curvilinear composition, stability
Mots-clés : układ wielowymiarowy, złożenie krzywoliniowe, stabilność 
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     author = {Dymkov, M. and Gaishun, I.},
     title = {Stability of {Multi-Dimensional} {Discrete} {Systems} {With} {Varying} {Structure}},
     journal = {International Journal of Applied Mathematics and Computer Science},
     pages = {789--799},
     publisher = {mathdoc},
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     number = {4},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IJAMCS_1999_9_4_a2/}
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Dymkov, M.; Gaishun, I. Stability of Multi-Dimensional Discrete Systems With Varying Structure. International Journal of Applied Mathematics and Computer Science, Tome 9 (1999) no. 4, pp. 789-799. http://geodesic.mathdoc.fr/item/IJAMCS_1999_9_4_a2/