On the stability of trajectories of a set of difference equations

TitleOn the stability of trajectories of a set of difference equations
Publication TypeJournal Article
Year of Publication2014
AuthorsMartynyuk, AA
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
Date Published5/2014

For a set of difference equations generated by the discretization of a set of differential equations with a Hukuhara derivative, the comparison principle with a Lyapunov matrix function and the sufficient conditions for the stability of a set of trajectories are established. The analysis is carried out on the basis of the Lyapunov matrix function with a special structure.

Keywordsdifference equations, stability, trajectories

1. Bhaskar T. G., Shaw M. Dynamic Systems and Applications, 2004, 13, No. 3/4: 479–485.
2. Lakshmikantham V., Leela S., Martynyuk A. A. Stability analysis of nonlinear systems. New York: Marcel Dekker, 1989.
3. Aleksandrov A. Yu., Zhabko A. P. Stability of difference systems. St.-Petersburg: SPb gos. un-t, 2003 (in Russian).
4. Martynyuk A. A. Stability of motion. The role of multicomponent Liapunov’s functions. Cambridge: Cambridge Scientific Publishers, 2007.