Abstract
This study develops a gradient-velocity framework for robust stability analysis of satellite communication systems operating under parametric uncertainty. The relevance of the research is determined by the fact that satellite communication channels are affected by signal attenuation, propagation delay, gain variation, and channel noise, which may reduce the reliability of signal transmission and cause undesirable transient responses. The purpose of the study is to formulate analytical conditions that guarantee not only asymptotic stability but also a monotonic aperiodic transient process. The proposed method extends the classical Lyapunov approach by including velocity-related information in the analysis of the derivative of the Lyapunov function. A state-space model of a satellite communication system with bounded uncertain parameters is considered. Numerical simulations performed in MATLAB show that the proposed approach ensures smooth convergence of state trajectories without oscillations over the admissible uncertainty range. Compared with the classical Lyapunov-based criterion, the gradient-velocity framework reduces conservatism and provides more predictable transient behavior. The practical significance of the results lies in their applicability to the design and analysis of reliable satellite communication systems.