Stability of Deterministic and Averaged Systems of Radiophysical Processes in UAV Microcontroller Systems

• Datum: 2026
• Hauptverfasser: Нікітін, Анатолій, Шведюк, Володимир
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Кам'янець-Подільський національний університет імені Івана Огієнка 2026
• Online Zugang: https://mcm-math.kpnu.edu.ua/article/view/360512
• Назва журналу: Mathematical and computer modelling. Series: Physical and mathematical sciences

The article presents a theoretical study and mathematical modeling of the stability of complex radiophysical processes occurring in microcontroller control systems of modern UAVs. The relevance of the work is due to the need to ensure stable operation of on-board electronics in conditions of intense electromagnetic interference and non-stationary loads. The object of the study is state vectors, which include the signal amplitude, carrier phase and microcontroller supply voltage level. The scientific novelty of the work lies in the application of the averaging principle to the analysis of evolutionary systems with fast Markov switching. This approach allowed us to move from complex stochastic models to an equivalent deterministic system that operates with parameters averaged over a stationary distribution: damping coefficient, instantaneous frequency and intensity of losses in the power supply circuit. The work uses a set of methods from the theory of stability of linear systems. By analyzing the eigenvalues of the coefficient matrix, the necessary conditions for process stabilization were established. Using the construction of the quadratic Lyapunov function, an original sufficient condition for the asymptotic stability of the averaged system was derived, which takes into account the cross-coupling between the amplitude and energy supply channels. A critical threshold of the intensity of this coupling was established, exceeding which leads to the loss of system stability even with the stability of its individual components. The results obtained have direct practical application in the development of filtering and voltage stabilization algorithms in UAV autopilot systems. The proposed analytical dependencies allow at the design stage to optimize the parameters of hardware filters and software means of protecting the microcontroller from failures caused by fluctuations in the radio signal and engine load.