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Paper details
Number 4 - December 1999
Volume 9 - 1999
Stability of multi-dimensional discrete systems with varying structure
Michael Dymkov, Ivan Gaishun
Abstract
A new class of multi-dimensional discrete systems with varying structure is introduced. The notions of total solvability, pt-boundedness, pt-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 pt-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