Journal of Modern Technology and Engineering

The main result of this article is the replacement of the Lyapunov Energy Function (LEF), which is a solution to the Lyapunov equation, with a quadratic form. This function consists of the most informative indicators of the system - the tracking error and its derivatives which allows for easy determination of the stability of nonlinear systems in real time. Moreover, to suppress uncertainties, a "high-gain coefficient" is used as a control multiplier, giving the system robust properties without compromising stability. A qualitative analysis using Matlab/Simulink, based on a "peak gyroscope" control example, demonstrated the effectiveness of the proposed approach. Currently, robust control methods for uncertain systems pose complex challenges both in terms of mathematical synthesis and practical implementation. This article shows that the use of a high open-loop gain (forcing) makes it possible to compensate for total uncertainty to an arbitrarily small value without violating stability. The High-Gain Robust Control (HGRC) method was first proposed by the Russian scientist M. Meerov. The obtained results in terms of tracking accuracy, response speed, and implementation simplicity demonstrate a high scientific and technical level.