arXiv subjects

Ivan Atamas

Publications and source records attributed to Ivan Atamas.

2 recordsLinked to original sources

arXiv2025

Integral gains for non-autonomous Wazewski systems

In this work we consider linear non-autonomous systems of Wazewski type on Hilbert spaces and provide a new approach to study their stability properties by means of a decomposition into subsystems and conditions implied on the interconnection properties. These conditions are of the small-gain type but the appoach is based on a conceptually new notion which we call integral gain. This notion is introduced for the first time in this paper. We compare our approach with known results from the literature and demonstrate advantages of our results.

math.DS↗

arXiv2023

Asymptotic stability conditions for linear coupled impulsive systems with time-invariant subsystems

This article proposes an approach to construct a Lyapunov function for a linear coupled impulsive system consisting of two time-invariant subsystems. In contrast to various variants of small-gain stability conditions for coupled systems, the asymptotic stability property of independent subsystems is not assumed. To analyze the asymptotic stability of a coupled system, the direct Lyapunov method is used in combination with the discretization method. The periodic case and the case when the Floquet theory is not applicable are considered separately. The main results are illustrated with examples.

math.DS↗