Abstract
This paper investigates the challenge of globally practically tracking a class of high-order nonlinear systems with time delay via feedback. The object of study is a nonlinear system, the main goal is to develop a control function that allows you to regulate the output data of the specified nonlinear system using a reference signal. The article publication is distinguished by its scientific novelty due to the study of a system in which the degree of the upper limit of nonlinearity is determined within a continuous interval. The system under examination exhibits a distinctive characteristic, wherein the extent of the upper boundary limitation of nonlinearity is defined within a continuous interval. We propose a customizable and delay-independent tracking controller designed to mitigate the impact of delay time non-linearity. This is achieved by generating a Lyapunov function using a generalized approach that involves incorporating a signum function and a power integrator. The resulting controller ensures the global boundedness of all states within the closed system, along with a sufficiently small control error over a finite time. Additionally, this work places emphasis on computer simulations to validate previously obtained results.