Matematika AdMaS

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Exponential stability of perturbed linear discrete systems
(Springer, 2016-01-29) Diblík, Josef; Khusainov, Denys; Baštinec, Jaromír; Sirenko, Andrii
The paper considers the problem of exponential stability and convergence rate to solutions of perturbed linear discrete homogeneous systems. New criteria on exponential stability are derived by using the second method of Lyapunov. We consider non-delayed systems as well as systems with a single delay. Simultaneously, explicit exponential estimates of the solutions are derived. The results are illustrated by examples.
Bounded and unbounded non-oscillatory solutions of a four-dimensional nonlinear neutral difference system
(Springer Nature, 2015-10-15) Diblík, Josef; Lupinska, Barbara; Růžičková, Miroslava; Zonenberg, Joanna
The paper is concerned with a four-dimensional nonlinear difference system with delayed arguments where the first equation of the system is of a neutral type. A classification of non-oscillatory solutions is given and results on their boundedness or unboundedness are derived. The results obtained are illustrated by examples.