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1 International Journal of Applied Mathematics and Computer Science

1 1999

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Stability of Multi-Dimensional Discrete Systems With Varying Structure

Dymkov M., Gaishun I.

International Journal of Applied Mathematics and Computer Science

1999

Vol. 9, no 4

789-799

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.